-
question_answer1)
If \[\cos ec\,\theta =\sqrt{10},\]then \[\sec \,\theta =\]
A)
\[\frac{3}{\sqrt{10}}\] done
clear
B)
\[\frac{\sqrt{10}}{3}\] done
clear
C)
\[\frac{1}{\sqrt{10}}\] done
clear
D)
\[\frac{2}{\sqrt{10}}\] done
clear
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question_answer2)
If in \[\Delta ABC,\] \[\angle B=90{}^\circ ,\] \[\text{AB}=\text{12 cm}\] and \[\text{BC}=\text{5 cm},\] then the value of \[cot\,C\] is:
A)
\[\frac{13}{5}\] done
clear
B)
\[\frac{5}{12}\] done
clear
C)
\[\frac{12}{5}\] done
clear
D)
\[\frac{5}{13}\] done
clear
View Solution play_arrow
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question_answer3)
If \[\sec \theta =\frac{25}{7},\] then \[\sin \theta =\]
A)
\[\frac{7}{24}\] done
clear
B)
\[\frac{24}{7}\] done
clear
C)
\[\frac{24}{25}\] done
clear
D)
\[\frac{25}{24}\] done
clear
View Solution play_arrow
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question_answer4)
The maximum value of \[\sin \theta \] is:
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{\sqrt{3}}{2}\] done
clear
C)
\[1\] done
clear
D)
\[\frac{1}{\sqrt{2}}\] done
clear
View Solution play_arrow
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question_answer5)
If A is an acute angle of a \[\Delta ABC,\]right angled at B, then the value of \[\sin A+\cos A\] is:
A)
equal to one done
clear
B)
greater than one done
clear
C)
less than one done
clear
D)
equal to two done
clear
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question_answer6)
If \[\tan \theta =\frac{3}{4},\]then \[{{\cos }^{2}}\theta -{{\sin }^{2}}\theta =\]
A)
\[\frac{7}{25}\] done
clear
B)
\[1\] done
clear
C)
\[\frac{-7}{25}\] done
clear
D)
\[\frac{4}{25}\] done
clear
View Solution play_arrow
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question_answer7)
If \[16\cot \,\,x=12,\] then \[\frac{\sin x-\cos x}{\sin x+\cos x}\] equals:
A)
\[\frac{1}{7}\] done
clear
B)
\[\frac{3}{7}\] done
clear
C)
\[\frac{2}{7}\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
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question_answer8)
If \[\tan \theta =\frac{a}{b},\]then \[\frac{(a\sin \theta -b\cos \theta )}{(a\sin \theta +b\cos \theta )}=\]
A)
\[\frac{({{a}^{2}}+{{b}^{2}})}{({{a}^{2}}-{{b}^{2}})}\] done
clear
B)
\[\frac{({{a}^{2}}-{{b}^{2}})}{({{a}^{2}}+{{b}^{2}})}\] done
clear
C)
\[\frac{{{a}^{2}}}{({{a}^{2}}+{{b}^{2}})}\] done
clear
D)
\[\frac{{{b}^{2}}}{({{a}^{2}}+{{b}^{2}})}\] done
clear
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question_answer9)
From the figurer, the value of \[25({{\sin }^{2}}\theta +2{{\cos }^{2}}\theta -\tan \theta )\] is |
|
A)
\[\frac{2}{3}\] done
clear
B)
\[-\frac{2}{3}\] done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[-\frac{3}{2}\] done
clear
View Solution play_arrow
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question_answer10)
In \[\Delta OPQ\] right-angled at P, \[OP=7cm,\]and \[OQ-PQ=1cm,\]then the value of \[\sin Q\] is: (NCERT Exercise)
A)
\[\frac{3}{25}\] done
clear
B)
\[\frac{1}{5}\] done
clear
C)
\[\frac{7}{25}\] done
clear
D)
\[\frac{9}{25}\] done
clear
View Solution play_arrow
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question_answer11)
In figure, \[\text{AD}=\text{4}\,\text{cm},\] \[\text{BD}=\text{3 cm}\] and \[\text{CB}=\text{12 cm},\]then the value of \[\cot \theta \] is:(CBSE 2016) |
|
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{12}{5}\] done
clear
C)
\[\frac{7}{5}\] done
clear
D)
\[\frac{5}{7}\] done
clear
View Solution play_arrow
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question_answer12)
If in a right-angled \[\Delta ACB,\] \[\tan \,B=\frac{12}{5},\] then \[\sin B\] is: (CBSE 2014)
A)
\[\frac{12}{13}\] done
clear
B)
\[\frac{5}{13}\] done
clear
C)
\[\frac{7}{13}\] done
clear
D)
\[\frac{9}{13}\] done
clear
View Solution play_arrow
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question_answer13)
If \[\sqrt{3}\sin \theta =\cos \theta ,\]then value of \[\frac{3{{\cos }^{2}}\theta +2\cos \theta }{3\cos \theta +2}\]is:
A)
\[\sqrt{3}\,\cos \theta \] done
clear
B)
\[3\,\cos \theta \] done
clear
C)
\[3\,\sin \theta \] done
clear
D)
\[\sqrt{3}\,\sin \theta \] done
clear
View Solution play_arrow
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question_answer14)
If \[\tan \theta +\cot \theta =5,\] then the value of \[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta \] is: (CBSE 2012)
A)
1 done
clear
B)
7 done
clear
C)
23 done
clear
D)
25 done
clear
View Solution play_arrow
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question_answer15)
In the given figure, if \[AB=14cm,\] then the value of tan B is:(CBSE 2012) |
|
A)
\[\frac{4}{3}\] done
clear
B)
\[\frac{14}{3}\] done
clear
C)
\[\frac{5}{3}\] done
clear
D)
\[\frac{13}{3}\] done
clear
View Solution play_arrow
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question_answer16)
Match the column:
Column I |
Column II |
1. |
\[\frac{\text{Side opposite to angle }\theta }{\text{Hypotenuse}}\] |
A. |
\[\tan \theta \] |
2. |
\[\frac{\text{Side adjacent to angle }\theta }{\text{Hypotenuse}}\] |
B. |
\[\sin \theta \] |
3. |
\[\frac{\text{Side opposite to angle }\theta }{\text{Side adjacent to angle }\theta }\] |
C. |
\[\sin \theta \] |
|
|
D. |
\[\sec \theta \] |
A)
1-A, 2-C, 3-B done
clear
B)
1-B, 2-C, 3-A done
clear
C)
1-B, 2-C, 3-D done
clear
D)
1-D, 2-B, 3-A done
clear
View Solution play_arrow
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question_answer17)
Match the column:
Column I | Column II |
1. | \[\cos ec\,\theta \] | A. | \[\cos ec\,\theta \] |
2. | \[\frac{\text{Side adjacent to angle }\theta }{\text{Side opposite to angle }\theta }\] | B. | \[\sec \theta \] |
3. | \[\frac{Hypotenuse}{\text{Side opposite to angle }\theta }\] | C. | \[\tan \theta \] |
| | D. | \[\cot \theta \] |
| | E. | \[\sin \theta \] |
A)
1-A, 2-C, 3-B done
clear
B)
1-C, 2-A, 3-D done
clear
C)
1-B, 2-A, 3-E done
clear
D)
1-B, 2-D, 3-A done
clear
View Solution play_arrow
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question_answer18)
If the angle remains the same, the value of the trigonometric ratios of the angle:
A)
vary with the length of the sides of the triangle. done
clear
B)
do not vary with the length of the sides of the triangle. done
clear
C)
vary with the change in length of hypotenuse only. done
clear
D)
do not vary with the change in length of hypotenuse only. done
clear
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question_answer19)
If \[\Delta ABC,\] right angled at B, \[\text{AC}=\text{13 cm},\] \[\text{AB}=\text{5 cm},\] then \[\sin A=\]
A)
\[\frac{5}{13}\] done
clear
B)
\[\frac{5}{12}\] done
clear
C)
\[\frac{12}{13}\] done
clear
D)
\[\frac{13}{12}\] done
clear
View Solution play_arrow
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question_answer20)
\[\sin A=\]
A)
\[\tan A-\cot A\] done
clear
B)
\[\frac{tan\,A}{\sec A}\] done
clear
C)
\[\tan A-\sec A\] done
clear
D)
\[\cos A-\sec A\] done
clear
View Solution play_arrow
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question_answer21)
If \[\text{sin x}+\text{cosec x}=\text{2},\]then \[{{\sin }^{19}}x+\text{cose}{{\text{c}}^{20}}x=\]
A)
\[{{2}^{19}}\] done
clear
B)
\[{{2}^{20}}\] done
clear
C)
\[2\] done
clear
D)
\[{{2}^{39}}\] done
clear
View Solution play_arrow
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question_answer22)
If \[\tan A+\cot A=4,\] then \[{{\tan }^{4}}A+{{\cot }^{4}}A=\]
A)
196 done
clear
B)
194 done
clear
C)
192 done
clear
D)
190 done
clear
View Solution play_arrow
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question_answer23)
If \[3\cot \theta =2,\] then the value of \[\tan \theta \] is:
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[\frac{3}{\sqrt{13}}\] done
clear
D)
\[\frac{2}{\sqrt{13}}\] done
clear
View Solution play_arrow
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question_answer24)
If \[\cos \theta =\frac{7}{8}\] then value of \[\sec \theta =\]
A)
\[\frac{8}{7}\] done
clear
B)
\[\frac{7}{\sqrt{113}}\] done
clear
C)
\[\frac{8}{\sqrt{113}}\] done
clear
D)
\[1\] done
clear
View Solution play_arrow
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question_answer25)
In \[\Delta PQR,\] right-angled at Q, \[\text{PR}+\text{QR}=\text{25 cm}\] and \[\text{PQ}=\text{5 cm}\]. The value of tan P is:
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{12}{5}\] done
clear
C)
\[\frac{7}{5}\] done
clear
D)
\[\frac{5}{7}\] done
clear
View Solution play_arrow
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question_answer26)
\[\sqrt{-4+\sqrt{8+16\,\text{cose}{{\text{c}}^{4}}\theta +{{\sin }^{4}}\theta }}=A\,\text{cosec}\theta \text{+Bsin}\theta \text{,}\] then A and B are:
A)
\[2\] and \[-1\] done
clear
B)
\[1\]and \[\frac{1}{2}\] done
clear
C)
\[\frac{1}{2}\]and \[\frac{1}{3}\] done
clear
D)
\[3\] and \[-4\] done
clear
View Solution play_arrow
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question_answer27)
If \[\tan \theta =\frac{a\sin \phi }{1-a\cos \phi }\]and \[\tan \phi =\frac{b\sin \theta }{1-b\cos \theta },\]then \[\frac{a}{b}=\]
A)
\[\frac{\sin \theta }{1-\cos \theta }\] done
clear
B)
\[\frac{\sin \theta }{1-\cos \phi }\] done
clear
C)
\[\frac{\sin \phi }{\sin \theta }\] done
clear
D)
\[\frac{\sin \theta }{\sin \phi }\] done
clear
View Solution play_arrow
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question_answer28)
If \[2\sin 2\theta =\sqrt{3},\]then \[\theta =\]
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow
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question_answer29)
In \[\Delta ABC,\] \[\angle B=90{}^\circ ,\] \[\angle A=30{}^\circ \]and \[AB=9\,cm\]. Then, \[BC=\] |
|
A)
\[3cm\] done
clear
B)
\[2\sqrt{3}cm\] done
clear
C)
\[3\sqrt{3}cm\] done
clear
D)
\[6\,cm\] done
clear
View Solution play_arrow
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question_answer30)
In the given figure, ABCD is a rectangle with \[AD=8cm\]and \[CD=12cm\]. Line segment CE is drawn, making an angle of \[60{}^\circ \]with AB, intersecting AB at E. Find the length of CE and BE respectively. |
|
A)
\[\frac{16}{\sqrt{3}}cm,\,\,\frac{8}{\sqrt{3}}cm\] done
clear
B)
\[\frac{8}{\sqrt{3}}cm,\,\,\frac{16}{\sqrt{3}}cm\] done
clear
C)
\[\frac{16}{\sqrt{3}}cm,\,\,\frac{7}{\sqrt{3}}cm\] done
clear
D)
\[\frac{8}{\sqrt{3}}cm,\,\,\frac{5}{\sqrt{3}}cm\] done
clear
View Solution play_arrow
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question_answer31)
The value of \[\frac{\sin 60{}^\circ +\cot 45{}^\circ -\text{cosec 30}{}^\circ }{\sec 60{}^\circ -\cos 30{}^\circ +\tan 45{}^\circ }\] is:
A)
\[\frac{4\sqrt{3}-9}{33}\] done
clear
B)
\[\frac{4\sqrt{3}+9}{33}\] done
clear
C)
\[\frac{9\sqrt{3}-4}{33}\] done
clear
D)
\[\frac{9\sqrt{3}+4}{33}\] done
clear
View Solution play_arrow
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question_answer32)
The value of \[\frac{{{\tan }^{2}}60{}^\circ +4{{\cos }^{2}}45{}^\circ +3{{\sec }^{2}}30{}^\circ }{\text{cosec 30}{}^\circ +\sec \,60{}^\circ -{{\cot }^{2}}30{}^\circ }\] is
A)
\[9\] done
clear
B)
\[\frac{1}{9}\] done
clear
C)
\[3\] done
clear
D)
\[\frac{1}{3}\] done
clear
View Solution play_arrow
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question_answer33)
If \[\cot \theta =\frac{1}{\sqrt{3}},\]then the value of \[\frac{1-{{\cos }^{2}}\theta }{2-{{\sin }^{2}}\theta }\] is:
A)
\[\frac{1}{5}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
\[\frac{5}{3}\] done
clear
View Solution play_arrow
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question_answer34)
In \[\Delta ABC,\] \[\angle B=90{}^\circ \]. If \[\tan A=\sqrt{3},\]then the value of \[\sin A.\cos C-\cos A.\sin C\] is:
A)
\[\frac{1}{2}\] done
clear
B)
\[-1\] done
clear
C)
\[1\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
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question_answer35)
If \[\text{cosec A = }\sqrt{2},\]then the value of \[\frac{2{{\sin }^{2}}A+3{{\cot }^{2}}A}{4({{\tan }^{2}}A-{{\cos }^{2}}A)}\] is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
0 done
clear
View Solution play_arrow
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question_answer36)
If \[{{\tan }^{2}}45{}^\circ -{{\cos }^{2}}30{}^\circ =x\sin 45{}^\circ \,\cos 45{}^\circ ,\] then \[x=\]
A)
\[2\] done
clear
B)
\[-2\] done
clear
C)
\[-\frac{1}{2}\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
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question_answer37)
If \[\frac{x\,\text{cose}{{\text{c}}^{2}}30{}^\circ \,\,{{\sec }^{2}}45{}^\circ }{8\,{{\cos }^{2}}45{}^\circ \,{{\sin }^{2}}60{}^\circ }={{\tan }^{2}}60{}^\circ -{{\tan }^{2}}30{}^\circ ,\]then \[x=\]
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[2\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
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question_answer38)
If \[\sin 2A=\frac{1}{2}{{\tan }^{2}}45{}^\circ ,\]where A is an acute angle, then the value of A is:
A)
\[60{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[30{}^\circ \] done
clear
D)
\[15{}^\circ \] done
clear
View Solution play_arrow
-
question_answer39)
Evaluate: \[8\sqrt{3}\,\,\text{cose}{{\text{c}}^{2}}30{}^\circ \,\sin 60{}^\circ \,\cos 60{}^\circ \,{{\cos }^{2}}45{}^\circ \,\sin 45{}^\circ \,\tan 30{}^\circ \] \[\text{cose}{{\text{c}}^{3}}45{}^\circ \]:
A)
\[8\] done
clear
B)
\[4\sqrt{3}\] done
clear
C)
\[8\sqrt{3}\] done
clear
D)
\[16\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer40)
If \[\tan \alpha =\sqrt{3}\] and \[\tan \beta =\frac{1}{\sqrt{3}},\] \[0<\alpha ,\] \[\beta <90{}^\circ ,\]then the value of \[\cot (\alpha +\beta )\] is:
A)
\[\sqrt{3}\] done
clear
B)
\[0\] done
clear
C)
\[\frac{1}{\sqrt{3}}\] done
clear
D)
\[1\] done
clear
View Solution play_arrow
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question_answer41)
If \[\cos \alpha =\frac{\sqrt{3}}{2}\]and \[\tan \beta =\frac{1}{\sqrt{3}},\]then the value of \[\sin (\alpha +\beta ),\] where \[\alpha \]and \[\beta \]both are acute angles is:
A)
\[\frac{1}{2}+\frac{1}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}+2\] done
clear
C)
\[\frac{\sqrt{3}}{2}\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
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question_answer42)
Given that \[\sin \alpha =\frac{1}{2}\]and \[\cos \beta =\frac{1}{2},\]then the vale of \[(\alpha +\beta )\]is:
A)
\[0{}^\circ \] done
clear
B)
\[30{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow
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question_answer43)
The value of \[(\sin 30{}^\circ +\cos 30{}^\circ )-(\sin 60{}^\circ +\cos 60{}^\circ )\] is: (NCERT EXEMPLAR)
A)
\[-1\] done
clear
B)
0 done
clear
C)
\[1\] done
clear
D)
\[2\] done
clear
View Solution play_arrow
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question_answer44)
The value of \[\frac{\tan 30{}^\circ }{\cot 60{}^\circ }\]is: (NCERT EXEMPLAR)
A)
\[\frac{1}{\sqrt{2}}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[1\] done
clear
View Solution play_arrow
-
question_answer45)
The value of \[(\sin 45{}^\circ +\cos 45{}^\circ )\] is: (NCERT EXEMPLAR)
A)
\[\frac{1}{\sqrt{2}}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[\frac{\sqrt{3}}{2}\] done
clear
D)
\[1\] done
clear
View Solution play_arrow
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question_answer46)
\[\sec \theta \]is always:
A)
less than one done
clear
B)
less than or equal to one done
clear
C)
greater than one done
clear
D)
greater than or equal to one done
clear
View Solution play_arrow
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question_answer47)
\[\frac{2\tan 30{}^\circ }{1+{{\tan }^{2}}30{}^\circ }\] is equal to: (NCERT EXEMPLAR)
A)
\[\sin 60{}^\circ \] done
clear
B)
\[\cos 60{}^\circ \] done
clear
C)
\[\tan 60{}^\circ \] done
clear
D)
\[\sin 30{}^\circ \] done
clear
View Solution play_arrow
-
question_answer48)
\[\frac{1-{{\tan }^{2}}45{}^\circ }{1+{{\tan }^{2}}45{}^\circ }\]is equal to: (NCERT EXEMPLAR)
A)
\[\tan 90{}^\circ \] done
clear
B)
\[1\] done
clear
C)
\[sin45{}^\circ \] done
clear
D)
0 done
clear
View Solution play_arrow
-
question_answer49)
\[\sin 2A=2\sin A\]is true when A is:(NCERT EXEMPLAR)
A)
\[0{}^\circ \] done
clear
B)
\[30{}^\circ \] done
clear
C)
\[45{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
View Solution play_arrow
-
question_answer50)
\[\frac{2\tan 30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\]is equal to: (NCERT EXEMPLAR)
A)
\[\cos 60{}^\circ \] done
clear
B)
\[\sin 60{}^\circ \] done
clear
C)
\[\tan 60{}^\circ \] done
clear
D)
\[\sin 30{}^\circ \] done
clear
View Solution play_arrow
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question_answer51)
The value of \[\sin \theta \]or \[\cos \theta \]never exceeds:
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[-1\] done
clear
D)
\[\infty \] done
clear
View Solution play_arrow
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question_answer52)
. In \[\Delta ABC\] right-angled at point B, if \[\tan A=\frac{1}{\sqrt{3}},\]then the value of \[\sin A.\cos C+\cos A.\sin C\]is: (NCERT EXEMPLAR)
A)
0 done
clear
B)
1 done
clear
C)
-1 done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer53)
The value of \[\tan \theta \]increases from \[0\]to \[\infty \]when \[\theta \]increases from
A)
\[0{}^\circ \]to \[180{}^\circ \] done
clear
B)
\[90{}^\circ \]to \[180{}^\circ \] done
clear
C)
\[0{}^\circ \]to \[90{}^\circ \] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer54)
The value of \[({{\tan }^{2}}60{}^\circ +{{\sin }^{2}}45{}^\circ )\]is:
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[\frac{5}{2}\] done
clear
D)
\[\frac{7}{2}\] done
clear
View Solution play_arrow
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question_answer55)
If \[\sin x+\cos y=1,\]\[x=30{}^\circ \]and y is an acute angle then the value of y is:
A)
\[15{}^\circ \] done
clear
B)
\[30{}^\circ \] done
clear
C)
\[45{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
View Solution play_arrow
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question_answer56)
If \[\sin \alpha =\frac{1}{2}\] and \[\tan \beta =\frac{1}{\sqrt{3}},\] \[\alpha >0{}^\circ ,\] \[\beta >0{}^\circ \] then the value of \[\cot \,(\alpha +\beta )\] is: (CBSE 2017)
A)
\[\frac{1}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}\] done
clear
C)
\[1\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
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question_answer57)
If \[\sin \theta -\cos \theta =0,\]then the value of \[{{\sin }^{4}}\theta +{{\cos }^{4}}\theta \]is:(CBSE 2017)
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[-\frac{1}{2}\] done
clear
View Solution play_arrow
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question_answer58)
The value of \[\frac{1-{{\cot }^{2}}45{}^\circ }{1+{{\sin }^{2}}45{}^\circ }.10\]is:
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[0\] done
clear
D)
\[10\] done
clear
View Solution play_arrow
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question_answer59)
If \[\sin A=\cos B=\frac{1}{2},\]then the value of \[\tan \frac{1}{2}(A+B)\] is:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[\infty \] done
clear
View Solution play_arrow
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question_answer60)
If \[\sqrt{2}\,\sin (60{}^\circ -\alpha )=1,\]then \[\alpha \] is: (CBSE 2011)
A)
\[45{}^\circ \] done
clear
B)
\[15{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[30{}^\circ \] done
clear
View Solution play_arrow
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question_answer61)
The maximum value of \[\frac{1}{\text{cosec }\theta }\] is: (CBSE 2011)
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[\frac{\sqrt{3}}{2}\] done
clear
D)
\[\frac{1}{\sqrt{2}}\] done
clear
View Solution play_arrow
-
question_answer62)
The value of \[{{\sin }^{2}}30{}^\circ -{{\cos }^{2}}30{}^\circ \] is: (CBSE 2011)
A)
\[-\frac{1}{2}\] done
clear
B)
\[\frac{\sqrt{3}}{2}\] done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[\frac{2}{3}\] done
clear
View Solution play_arrow
-
question_answer63)
\[2{{\cos }^{2}}30{}^\circ -1=\]
A)
\[\sin 60{}^\circ \] done
clear
B)
\[\cos 60{}^\circ \] done
clear
C)
\[\tan 60{}^\circ \] done
clear
D)
\[\sec 60{}^\circ \] done
clear
View Solution play_arrow
-
question_answer64)
\[\tan 60{}^\circ =\]
A)
\[\frac{2\cos 30{}^\circ }{1-{{\cos }^{2}}30{}^\circ }\] done
clear
B)
\[\frac{2\tan 30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\] done
clear
C)
\[\frac{2\cot 30{}^\circ }{1-{{\cot }^{2}}30{}^\circ }\] done
clear
D)
\[2\,\sin 60{}^\circ \] done
clear
View Solution play_arrow
-
question_answer65)
In a right triangle, the hypotenuse is 2 times as long as its one side. One of the acute angle is:
A)
\[45{}^\circ \] done
clear
B)
\[30{}^\circ \] done
clear
C)
\[75{}^\circ \] done
clear
D)
\[25{}^\circ \] done
clear
View Solution play_arrow
-
question_answer66)
If \[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta =2,\] \[\theta \]is an acute angle, then \[{{\tan }^{3}}\theta +{{\cot }^{3}}\theta \] is equal to:
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
8 done
clear
View Solution play_arrow
-
question_answer67)
Which of the following is incorrect (\[\theta \]is acute angle)?
A)
\[\tan \theta =3\] done
clear
B)
\[\sin \theta =3\] done
clear
C)
\[\sec \theta =3\] done
clear
D)
\[\cot \theta =3\] done
clear
View Solution play_arrow
-
question_answer68)
Which of the following is possible?
A)
\[\cos \theta =\frac{7}{5}\] done
clear
B)
\[\sin \theta =\frac{13}{12}\] done
clear
C)
\[\sec \theta =\frac{4}{5}\] done
clear
D)
\[\tan \theta =41\] done
clear
View Solution play_arrow
-
question_answer69)
If \[0{}^\circ <\theta <90{}^\circ ,\]then \[\sec \theta \]is:
A)
\[>1\] done
clear
B)
\[<1\] done
clear
C)
\[=1\] done
clear
D)
\[0\] done
clear
View Solution play_arrow
-
question_answer70)
If \[\sin A=\cos A,\] \[0{}^\circ <A<90{}^\circ ,\] then A is equal to:
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow
-
question_answer71)
If \[\sin \theta =\sqrt{3}\,\,\cos \theta ,\]\[0{}^\circ <\theta <90{}^\circ ,\]then \[\theta \]is equal to:
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow
-
question_answer72)
\[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]is equal to:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[-1\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer73)
If \[\tan \theta =\frac{1}{\sqrt{7}},\]then \[\frac{(\text{cose}{{\text{c}}^{2}}\theta -{{\sec }^{2}}\theta )}{(\text{cose}{{\text{c}}^{2}}\theta +{{\sec }^{2}}\theta )}=\]
A)
\[\frac{-2}{3}\] done
clear
B)
\[\frac{-3}{4}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{3}{4}\] done
clear
View Solution play_arrow
-
question_answer74)
If \[\theta\] is an acute angle such that \[{{\tan }^{2}}\theta =\frac{8}{7},\]then the value of \[\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}\] is:
A)
\[\frac{7}{8}\] done
clear
B)
\[\frac{8}{7}\] done
clear
C)
\[\frac{7}{4}\] done
clear
D)
\[\frac{64}{49}\] done
clear
View Solution play_arrow
-
question_answer75)
If \[a\,\cos \theta +b\sin \theta =m\] and \[a\,\sin \theta -b\cos \theta =n,\]then \[{{a}^{2}}+{{b}^{2}}=\]
A)
\[{{m}^{2}}-{{n}^{2}}\] done
clear
B)
\[{{n}^{2}}-{{m}^{2}}\] done
clear
C)
\[{{m}^{2}}+{{n}^{2}}\] done
clear
D)
\[{{m}^{2}}{{n}^{2}}\] done
clear
View Solution play_arrow
-
question_answer76)
If \[\tan \theta +\cot \theta =2,\] then \[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta \] equals:
A)
4 done
clear
B)
6 done
clear
C)
2 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer77)
If \[x=a\,\sec \theta \,\cos \phi ,\]\[y=b\sec \theta \sin \phi \]and \[z=c\tan \theta ,\]then \[\left( \frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}} \right)=\]
A)
\[\left( 1+\frac{{{z}^{2}}}{{{c}^{2}}} \right)\] done
clear
B)
\[\left( 1-\frac{{{z}^{2}}}{{{c}^{2}}} \right)\] done
clear
C)
\[\left( \frac{{{z}^{2}}}{{{c}^{2}}}-1 \right)\] done
clear
D)
\[\frac{{{z}^{2}}}{{{c}^{2}}}\] done
clear
View Solution play_arrow
-
question_answer78)
If \[a\,\cot \theta +b\,\text{cosec }\theta \,\text{= p}\]and \[b\,\cot \theta +a\,\text{cosec }\theta \,\text{= q,}\] then \[{{p}^{2}}-{{q}^{2}}=\]
A)
\[{{a}^{2}}-{{b}^{2}}\] done
clear
B)
\[{{b}^{2}}-{{a}^{2}}\] done
clear
C)
\[{{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[b-a\] done
clear
View Solution play_arrow
-
question_answer79)
If \[2x=\sec \theta \] and \[\frac{2}{x}=\tan \theta ,\] then \[2\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)=\]
A)
\[\frac{1}{2}\] done
clear
B)
\[2\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[4\] done
clear
View Solution play_arrow
-
question_answer80)
If \[{{\tan }^{2}}A=1+2{{\tan }^{2}}B,\] then \[\frac{{{\cos }^{2}}A}{{{\cos }^{2}}B}=\]
A)
\[1\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{\sqrt{3}}{2}\] done
clear
View Solution play_arrow
-
question_answer81)
\[\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}\] is equal to:
A)
\[\text{cosec}\,\theta -\cot \theta \] done
clear
B)
\[\text{cosec}\,\theta +\cot \theta \] done
clear
C)
\[\text{cose}{{\text{c}}^{2}}\,\theta +{{\cot }^{2}}\theta \] done
clear
D)
\[\text{cose}{{\text{c}}^{2}}\,\theta -{{\cot }^{2}}\theta \] done
clear
View Solution play_arrow
-
question_answer82)
If \[x=a\,\tan \theta \]and \[y=b\,\sec \theta ,\] then:
A)
\[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] done
clear
B)
\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] done
clear
C)
\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] done
clear
D)
\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=0\] done
clear
View Solution play_arrow
-
question_answer83)
\[({{\sec }^{4}}A-{{\sec }^{2}}A)=\]
A)
\[{{\tan }^{4}}A-{{\tan }^{2}}A\] done
clear
B)
\[{{\tan }^{2}}A+{{\tan }^{4}}A\] done
clear
C)
\[{{\tan }^{2}}A-{{\tan }^{4}}A\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer84)
Evaluate: \[\sqrt{\frac{\sec \theta -1}{\sec \theta +1}}+\sqrt{\frac{\sec \theta +1}{\sec \theta -1}}\]
A)
\[2\sin \theta \] done
clear
B)
\[2\cos \theta \] done
clear
C)
\[2\text{cosec}\theta \] done
clear
D)
\[2\text{sec }\theta \] done
clear
View Solution play_arrow
-
question_answer85)
\[\frac{\sin \theta }{(1-\cot \theta )}+\frac{\cos \theta }{(1-\tan \theta )}\] is equal to:
A)
\[(\cos \theta +\sin \theta )\] done
clear
B)
\[(\cos \theta -\sin \theta )\] done
clear
C)
\[0\] done
clear
D)
\[2\tan \theta \] done
clear
View Solution play_arrow
-
question_answer86)
If \[\cos A=\frac{4}{5},\]then the value of \[\tan A\] is: (NCERT EXEMPLAR)
A)
\[\frac{3}{5}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[\frac{5}{3}\] done
clear
View Solution play_arrow
-
question_answer87)
If \[\sin A=\frac{1}{2},\]then the value of \[\cot A\] is: (NCERT EXEMPLAR)
A)
\[\sqrt{3}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\frac{\sqrt{3}}{2}\] done
clear
D)
\[1\] done
clear
View Solution play_arrow
-
question_answer88)
Given that \[\sin \theta =\frac{a}{b},\]then \[\cos \theta \] is equal to: (NCERT EXEMPLAR)
A)
\[\frac{b}{\sqrt{{{b}^{2}}-{{a}^{2}}}}\] done
clear
B)
\[\frac{b}{a}\] done
clear
C)
\[\frac{\sqrt{{{b}^{2}}-{{a}^{2}}}}{b}\] done
clear
D)
\[\frac{a}{\sqrt{{{b}^{2}}-{{a}^{2}}}}\] done
clear
View Solution play_arrow
-
question_answer89)
If \[\sin A+{{\sin }^{2}}A=1,\]then the value of the expression \[({{\cos }^{2}}A+{{\cos }^{4}}A)\] is (NCERT EXEMPLAR; CBSE 2020)
A)
\[1\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[2\] done
clear
D)
\[3\] done
clear
View Solution play_arrow
-
question_answer90)
\[9{{\sec }^{2}}A-9{{\tan }^{2}}A\]is equal to: (NCERT EXEMPLAR)
A)
1 done
clear
B)
9 done
clear
C)
8 done
clear
D)
0 done
clear
View Solution play_arrow
-
question_answer91)
\[\frac{1+{{\tan }^{2}}A}{1+{{\cot }^{2}}A}\]is equal to:
A)
\[{{\sec }^{2}}A\] done
clear
B)
\[-1\] done
clear
C)
\[{{\cot }^{2}}A\] done
clear
D)
\[{{\tan }^{2}}A\] done
clear
View Solution play_arrow
-
question_answer92)
\[(\sec A+\tan A)\,\,(1-\sin A)\]is equal to: (NCERT EXEMPLAR)
A)
\[\sec A\] done
clear
B)
\[\sin A\] done
clear
C)
\[\text{cosec A}\] done
clear
D)
\[\text{cos A}\] done
clear
View Solution play_arrow
-
question_answer93)
\[(1+\tan \theta +\sec \theta )\,\,(1+\cot \theta -\text{cosec }\theta \text{)}\] is equal to: (NCERT EXEMPLAR)
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
-1 done
clear
View Solution play_arrow
-
question_answer94)
The value of \[\theta \] in \[5{{\sin }^{2}}\theta -{{\cos }^{2}}\theta =2\] is:
A)
\[30{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[60{}^\circ \] done
clear
D)
\[90{}^\circ \] done
clear
View Solution play_arrow
-
question_answer95)
If \[7{{\sin }^{2}}A+3{{\cos }^{2}}A=4,\] then \[\tan A\] is equal to:
A)
\[\sqrt{3}\] done
clear
B)
\[1\] done
clear
C)
\[0\] done
clear
D)
\[\frac{1}{\sqrt{3}}\] done
clear
View Solution play_arrow
-
question_answer96)
If \[\sin \theta =\frac{5}{18},\] then the value of \[\tan \theta \] is: (CBSE 2020)
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{7}{12}\] done
clear
C)
\[\frac{3}{4}\] done
clear
D)
\[\frac{11}{12}\] done
clear
View Solution play_arrow
-
question_answer97)
If \[\sec \theta +\tan \theta =7,\]then \[(\sec \theta -\tan \theta )\] is equal to: (CBSE 2012)
A)
7 done
clear
B)
0 done
clear
C)
\[\frac{1}{7}\] done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer98)
If \[\tan \theta =\frac{a}{x},\]then the value of \[\frac{x}{\sqrt{{{a}^{2}}+{{x}^{2}}}}\] is:
A)
\[\sin \theta \] done
clear
B)
\[\sec \theta \] done
clear
C)
\[\cos \theta \] done
clear
D)
\[\text{cosec}\theta \] done
clear
View Solution play_arrow
-
question_answer99)
If \[\text{cosec}\theta -\cot \theta =\frac{1}{3},\]the value of \[\text{(cosec}\theta +\cot \theta )\] is: (CBSE 2011)
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer100)
If \[\sin A=\frac{4}{5},\] then \[1-2{{\sin }^{2}}A=\]
A)
\[1-2{{\cos }^{2}}A\] done
clear
B)
\[{{\cos }^{2}}A-{{\sin }^{2}}A\] done
clear
C)
\[2{{\sin }^{2}}A+1\] done
clear
D)
\[{{\sin }^{2}}A-{{\cos }^{2}}A\] done
clear
View Solution play_arrow
-
question_answer101)
\[\tan A=\]
A)
\[\frac{\cos A}{\sqrt{1-{{\cos }^{2}}A}}\] done
clear
B)
\[\frac{\sec A}{\sqrt{1-{{\sec }^{2}}A}}\] done
clear
C)
\[\frac{\sin A}{\sqrt{1-{{\sin }^{2}}A}}\] done
clear
D)
\[\frac{1}{\sqrt{1-{{\sin }^{2}}A}}\] done
clear
View Solution play_arrow
-
question_answer102)
\[\sec A=\]
A)
\[\frac{1}{\cot A}\] done
clear
B)
\[\frac{1}{\text{cosec}A}\] done
clear
C)
\[\frac{1}{\sqrt{1+{{\cot }^{2}}A}}\] done
clear
D)
\[\frac{\sqrt{1+{{\cot }^{2}}A}}{\cot A}\] done
clear
View Solution play_arrow
-
question_answer103)
\[\frac{1+{{\cot }^{2}}A}{1+{{\tan }^{2}}A}=\]
A)
\[{{\tan }^{2}}A\] done
clear
B)
\[{{\sec }^{2}}A\] done
clear
C)
\[\text{cose}{{\text{c}}^{2}}A-1\] done
clear
D)
\[1-{{\sin }^{2}}A\] done
clear
View Solution play_arrow
-
question_answer104)
If \[\sec A+\tan A=x,\] then \[\tan A=\]
A)
\[\frac{2}{x}\] done
clear
B)
\[\frac{1}{2x}\] done
clear
C)
\[\frac{{{x}^{2}}-1}{2x}\] done
clear
D)
\[\frac{2x}{{{x}^{2}}-1}\] done
clear
View Solution play_arrow
-
question_answer105)
If \[\cos ec\,A-\cot A=\frac{4}{5},\] then \[\cos ec\,A=\]
A)
\[\frac{47}{40}\] done
clear
B)
\[\frac{59}{40}\] done
clear
C)
\[\frac{51}{40}\] done
clear
D)
\[\frac{41}{40}\] done
clear
View Solution play_arrow
-
question_answer106)
If \[x=(\sec A-\tan A)\,(\sec B-\tan B)\,(\sec C-\tan C)\] \[=(\sec A+\tan A)(\sec B+\tan B)(\sec C+\tan C),\] then \[x=\]
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[-1\] done
clear
D)
\[\pm 1\] done
clear
View Solution play_arrow
-
question_answer107)
If \[\cos ec\,\theta -\cot \theta =\frac{1}{2},\] \[0<\theta <\frac{\pi }{2},\] then \[\cos \theta =\]
A)
\[\frac{5}{3}\] done
clear
B)
\[\frac{3}{5}\] done
clear
C)
\[\frac{2}{5}\] done
clear
D)
\[\frac{4}{5}\] done
clear
View Solution play_arrow
-
question_answer108)
If \[x=r\,\sin \theta .\cos \phi ,\] \[y=r\sin \theta .\sin \phi \]and \[z=r\,\cos \theta ,\]then the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\]is independent of:
A)
\[r,\theta \] done
clear
B)
\[r,\phi \] done
clear
C)
\[\theta ,\phi \] done
clear
D)
\[r\] done
clear
View Solution play_arrow
-
question_answer109)
If \[\sin \theta \]and \[\cos \theta \] are the roots of the equation \[a{{x}^{2}}-bx+c=0,\] then \[a,b,c\] satisfy the relation:
A)
\[{{b}^{2}}-{{a}^{2}}=2ac\] done
clear
B)
\[{{a}^{2}}-{{b}^{2}}=2ac\] done
clear
C)
\[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\] done
clear
D)
\[{{a}^{2}}+{{b}^{2}}=2ac\] done
clear
View Solution play_arrow
-
question_answer110)
Value of \[(\cos ec\,A+\cot A)\,\,(1-\cos A)=\]
A)
\[\sec A\] done
clear
B)
\[\sin A\] done
clear
C)
\[\cos ecA\] done
clear
D)
\[\cos A\] done
clear
View Solution play_arrow
-
question_answer111)
Value of \[(1+\sin A)\,(\sec A-\tan A)=\]
A)
\[\sin A\] done
clear
B)
\[\cos A\] done
clear
C)
\[\tan A\] done
clear
D)
\[\sec A\] done
clear
View Solution play_arrow
-
question_answer112)
If \[(\tan \theta +2)(2\tan \theta +1)=A\tan \theta +B{{\sec }^{2}}\theta ,\] then AB is:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[-1\] done
clear
D)
\[10\] done
clear
View Solution play_arrow
-
question_answer113)
If \[\sqrt{(1-{{\cos }^{2}}\theta ){{\sec }^{2}}\theta }=k\,\tan \theta \]and \[0<\theta <90{}^\circ ,\] then k is:
A)
\[-1\] done
clear
B)
\[1\] done
clear
C)
\[2\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer114)
If \[\frac{1}{1+\sin \theta }+\frac{1}{1-\sin \theta }=k{{\sec }^{2}}\theta ,\] then the value of k is:
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[2\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer115)
If \[\frac{{{\tan }^{3}}\theta -1}{\tan \theta -1}=A\,{{\sec }^{2}}\theta +B\tan \theta ,\] then \[A+B\] is equal to:
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[2\] done
clear
D)
\[3\] done
clear
View Solution play_arrow
-
question_answer116)
If \[\sec \theta +\tan \theta =m,\] then the value of \[{{\sec }^{4}}\theta -{{\tan }^{4}}\theta -2\sec \theta \,\tan \theta \] is:
A)
\[{{m}^{2}}\] done
clear
B)
\[\frac{1}{{{m}^{2}}}\] done
clear
C)
\[\frac{1}{m}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer117)
If \[sin\,\theta -\cos \theta =\frac{3}{5},\]the \[\sin \theta .\cos \theta \] is equal to:
A)
\[\frac{3}{7}\] done
clear
B)
\[\frac{8}{25}\] done
clear
C)
\[\frac{7}{25}\] done
clear
D)
\[\frac{13}{25}\] done
clear
View Solution play_arrow
-
question_answer118)
The value of \[\frac{{{\sin }^{4}}\theta -{{\cos }^{4}}\theta }{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }\]is:
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer119)
If \[x=p\sec \theta \] and \[y=q\tan \theta ,\] then:
A)
\[{{x}^{2}}-{{y}^{2}}={{p}^{2}}{{q}^{2}}\] done
clear
B)
\[{{x}^{2}}{{q}^{2}}-{{y}^{2}}{{p}^{2}}=pq\] done
clear
C)
\[{{x}^{2}}{{q}^{2}}-{{y}^{2}}{{p}^{2}}=\frac{1}{{{p}^{2}}{{q}^{2}}}\] done
clear
D)
\[{{x}^{2}}{{q}^{2}}-{{y}^{2}}{{p}^{2}}={{p}^{2}}{{q}^{2}}\] done
clear
View Solution play_arrow
-
question_answer120)
\[({{\cos }^{4}}A-{{\sin }^{4}}A)\] is equal to:
A)
\[1-2{{\cos }^{2}}A\] done
clear
B)
\[2{{\sin }^{2}}A-1\] done
clear
C)
\[{{\sin }^{2}}A-{{\cos }^{2}}A\] done
clear
D)
\[2{{\cos }^{2}}A-1\] done
clear
View Solution play_arrow
-
question_answer121)
If \[x{{\sin }^{3}}\theta +y{{\cos }^{3}}\theta =\sin \theta \cos \theta \]and \[x\sin \theta =y\cos \theta ,\]than \[{{x}^{2}}+{{y}^{2}}\] is equal to:
A)
\[0\] done
clear
B)
\[1/2\] done
clear
C)
\[1\] done
clear
D)
\[3/2\] done
clear
View Solution play_arrow
-
question_answer122)
If \[\tan \theta +\sin \theta =m\] and \[\tan \theta -\sin \theta =n,\] then \[{{m}^{2}}-{{n}^{2}}\] is equal to:
A)
\[\sqrt{mn}\] done
clear
B)
\[\sqrt{\frac{m}{n}}\] done
clear
C)
\[4\sqrt{mn}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer123)
If \[0<\theta <\frac{\pi }{4},\] then the simplest from of \[\sqrt{1-2\sin \theta \cos \theta }\] is:
A)
\[\sin \theta -\cos \theta \] done
clear
B)
\[\cos \theta -\sin \theta \] done
clear
C)
\[\cos \theta +\sin \theta \] done
clear
D)
\[\sin \theta \,\cos \theta \] done
clear
View Solution play_arrow
-
question_answer124)
The value of \[(\text{cose}{{\text{c}}^{2}}\theta -1){{\tan }^{2}}\theta \] is: (CBSE 2016)
A)
\[-1\] done
clear
B)
\[1\] done
clear
C)
\[\cot \theta \] done
clear
D)
\[\sec \theta \] done
clear
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