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question_answer1)
\[\frac{{{\sec }^{2}}\theta -1}{{{\tan }^{2}}\theta }=?\]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
5 done
clear
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question_answer2)
\[\frac{3-4{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }+{{\tan }^{2}}\theta \] is
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
None of these done
clear
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question_answer3)
Find the value of, \[\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}+\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}\]
A)
\[2\sec \theta \] done
clear
B)
\[\sec \theta \] done
clear
C)
\[2co\sec \theta \] done
clear
D)
None of these done
clear
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question_answer4)
If \[\tan \theta =\frac{a}{b}\], find the value of \[\frac{\text{a}\,\sin \theta -b\cos \theta }{\text{a}\sin \theta +b\,cos\theta }\]
A)
\[\frac{{{\text{a}}^{\text{2}}}\text{-}{{\text{b}}^{\text{2}}}}{{{\text{a}}^{\text{2}}}\text{+}{{\text{b}}^{\text{2}}}}\] done
clear
B)
\[\frac{{{b}^{\text{2}}}\text{-}{{\text{a}}^{\text{2}}}}{{{b}^{\text{2}}}\text{+}{{\text{a}}^{\text{2}}}}\] done
clear
C)
\[\frac{{{a}^{\text{2}}}\text{+}{{\text{b}}^{\text{2}}}}{{{a}^{\text{2}}}\text{-}\,{{\text{b}}^{\text{2}}}}\] done
clear
D)
None of these done
clear
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question_answer5)
If \[cos\theta +sin\theta =\sqrt{2}\,cos\theta \], then \[cos\theta -sin\theta =\]
A)
\[\sqrt{2}\cos \theta \] done
clear
B)
\[\sqrt{2}sin\theta \] done
clear
C)
\[cos\theta \] done
clear
D)
None of these done
clear
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question_answer6)
Which of the following is possible?
A)
\[cos\theta =x+\frac{1}{x}\] done
clear
B)
\[sec\theta =\frac{{{x}^{2}}}{1+{{x}^{2}}}\] done
clear
C)
\[cosec\theta =\frac{{{x}^{2}}}{1+{{x}^{2}}}\] done
clear
D)
\[\tan \theta =\frac{{{x}^{2}}+x+1}{{{x}^{2}}-3x+5}\] done
clear
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question_answer7)
If tan \[\theta =\frac{x}{y}\], where x and y are whole numbers, find \[\sin \theta \].
A)
\[\frac{y}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done
clear
B)
\[\frac{x}{\sqrt{{{x}^{2}}-{{y}^{2}}}}\] done
clear
C)
\[\frac{y}{\sqrt{{{x}^{2}}+{{y}^{2}}}}\] done
clear
D)
\[\frac{x}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done
clear
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question_answer8)
If \[\text{sin A+si}{{\text{n}}^{\text{2}}}\text{ A=1}\], find the value of the expression \[(co{{s}^{2}}A+co{{s}^{4}}A)\].
A)
\[1\] done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[2\] done
clear
D)
\[3\] done
clear
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question_answer9)
If \[\frac{\sin \theta +cos\theta }{\sin \theta -\cos \theta }=\frac{\sqrt{3}+1}{\sqrt{3}-1}\], find the acute angle \[\theta \].
A)
\[90{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[30{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
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question_answer10)
\[\frac{1}{1+\sin \theta }+\frac{1}{1-\sin \theta }\] is equal to
A)
\[2{{\sec }^{2}}\theta \] done
clear
B)
\[2co{{s}^{2}}\theta \] done
clear
C)
\[0\] done
clear
D)
\[1\] done
clear
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question_answer11)
\[\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }+\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }=\]
A)
\[\frac{2}{1-2\,{{\cos }^{2}}\theta }\] done
clear
B)
\[\frac{2}{2\,{{\sin }^{2}}\theta -1}\] done
clear
C)
both (a) & (b) done
clear
D)
None of these done
clear
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question_answer12)
If \[\frac{1+\sin \alpha }{1-\sin \alpha }=\frac{{{m}^{2}}}{{{n}^{2}}},\] then sin \[\alpha \] is:
A)
\[\frac{{{m}^{2}}+{{n}^{2}}}{{{m}^{2}}-{{n}^{2}}}\] done
clear
B)
\[\frac{{{m}^{2}}-{{n}^{2}}}{{{m}^{2}}+{{n}^{2}}}\] done
clear
C)
\[\frac{{{m}^{2}}+{{n}^{2}}}{{{n}^{2}}+{{m}^{2}}}\] done
clear
D)
\[\frac{{{n}^{2}}-{{m}^{2}}}{{{m}^{2}}+{{n}^{2}}}\] done
clear
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question_answer13)
If \[sec\theta +tan\theta =2\], then find the value of sin \[\theta \].
A)
\[\frac{3}{5}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[-\frac{3}{5}\] done
clear
D)
\[-\frac{2}{5}\] done
clear
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question_answer14)
\[\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=\]_________
A)
\[sec\theta +tan\theta \] done
clear
B)
\[sec\theta -cot\theta \] done
clear
C)
\[cosec\theta +tan\theta \] done
clear
D)
\[cosec\theta -tan\theta \] done
clear
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question_answer15)
What is the value of \[\tan \theta \] in the adjoining figure?
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{4}{3}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[\frac{5}{12}\] done
clear
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question_answer16)
In the given fig. What is the value of \[\cos \phi \]?
A)
\[\frac{4}{5}\] done
clear
B)
\[\frac{3}{5}\] done
clear
C)
\[\frac{2}{5}\] done
clear
D)
\[\frac{2}{3}\] done
clear
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question_answer17)
If \[x=m\text{ }sin\theta \] and \[y=n\text{ }cos\theta \], What is the value of \[{{n}^{2}}{{x}^{2}}+{{m}^{2}}{{y}^{2}}\]?
A)
\[mn\] done
clear
B)
\[m{{n}^{2}}\] done
clear
C)
\[1\] done
clear
D)
\[{{m}^{2}}{{n}^{2}}\] done
clear
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question_answer18)
If \[\frac{\cos \,\,20{}^\circ }{\sin \,\,70{}^\circ }+\frac{2\,\cos \theta }{\sin (90{}^\circ -\theta )}=\frac{k}{2}\], what is the value of k?
A)
4 done
clear
B)
5 done
clear
C)
6 done
clear
D)
1 done
clear
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question_answer19)
Which of the following is equal to \[2\,\,ta{{n}^{2}}A-2\,\,se{{c}^{2}}A-5\,\,co{{t}^{2}}A+5\,\,\cos e{{c}^{2}}A\]?
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer20)
Which of the following is equal to a\[\left( 1+ta{{n}^{2}}\theta \right)\]\[\left( 1-sin\theta \right)\left( 1+sin\theta \right)\left( 1+cos\theta \right)\left( 1-cos\theta \right)\]\[\left( 1+co{{t}^{2}}\theta \right)\]?
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
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question_answer21)
If \[1+2\,si{{n}^{2}}\theta \,\,co{{s}^{2}}\theta =si{{n}^{2}}\theta +co{{s}^{2}}\theta +4\,k\,\,si{{n}^{2}}\theta \] \[co{{s}^{2}}\theta \] what is the value of k?
A)
1 done
clear
B)
? 1 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{-1}{2}\] done
clear
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question_answer22)
Which of the following is equal to \[\sin \theta \cos \theta -\frac{\sin \theta \cos (90{}^\circ -\theta )cos\theta }{\sec (90{}^\circ -\theta )}\]\[-\frac{\cos \theta \sin (90{}^\circ -\theta )sin\theta }{\cos ec(90{}^\circ -\theta )}?\]
A)
1 done
clear
B)
0 done
clear
C)
? 1 done
clear
D)
? 2 done
clear
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question_answer23)
If\[cos\,\theta +sec\,\theta =2\]. Which of the following is equal to \[co{{s}^{3}}\theta +se{{c}^{3}}\theta \]?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer24)
If\[sin\text{ }A+cosec\,\,A=2\], then what is the value of the value of \[\frac{{{\sin }^{4}}A+1}{{{\sin }^{2}}A}\]?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
\[6/\sqrt{2}\] done
clear
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question_answer25)
A vertical tower is surmounted by a flagstaff of height h metres. At a point on the ground, the angels of elevation of the bottom and top of the flagstaff are \[\alpha \] and \[\beta \] respectively. What is the height of the tower in meters?
A)
\[\frac{h\,\,\tan \,\,\alpha }{\tan \,\,\beta +\tan \,\,\alpha }\] done
clear
B)
\[\frac{h\,\,\tan \,\,\alpha }{\tan \,\,\beta -\tan \,\,\alpha }\] done
clear
C)
\[\frac{h\,\,\tan \,\,\alpha }{\tan \,\,\beta }\] done
clear
D)
\[\frac{h\,\,\tan \,\,\beta }{\tan \,\,\beta -\tan \,\,\alpha }\] done
clear
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question_answer26)
A round balloon of radius r subtends an angle \[\alpha \] at the eye of the observer while the angle of elevation of its center is\[\beta \]. What is the height of the center of the balloon?
A)
\[r\,\,\sin \,\,\beta \,\,\sec \frac{\alpha }{2}\] done
clear
B)
\[r\,\,\sin \,\,\beta \,\,cos\frac{\alpha }{2}\] done
clear
C)
\[r\,\,\sin \,\,\beta \,\,cosec\frac{\alpha }{2}\] done
clear
D)
\[r\,\,\cos \,\,\beta \,\,cosec\frac{\alpha }{2}\] done
clear
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question_answer27)
If the angle of elevation of a cloud from a point h metres above a lake is \[\alpha \] and the angle of depression of its reflection in the lake is \[\beta \], What is the distance of the cloud from the point of observation? (in ?m?)
A)
1 done
clear
B)
\[\frac{h(tan\,\beta -tan\,\alpha )}{\tan \,\beta +\tan \,\alpha }\] done
clear
C)
\[\frac{h(tan\,\beta +tan\,\alpha )}{\tan \,\beta -\tan \,\alpha }\] done
clear
D)
None of these done
clear
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question_answer28)
A 1.5 m tall boy is standing at some distance from a 63/2 m tall building. The angle of elevation from his eyes to the top of the building increases from \[30{}^\circ \] to \[60{}^\circ \] as he walks towards the building. What is the distance he walked towards the building?
A)
\[\frac{20}{\sqrt{3}}m\] done
clear
B)
\[30\sqrt{3}m\] done
clear
C)
\[20\sqrt{3}m\] done
clear
D)
\[\frac{30}{\sqrt{3}}m\] done
clear
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question_answer29)
If \[sec\,\,\theta +tan\,\,\theta =m\] and \[sec\text{ }\theta -tan\text{ }\theta =n\] then what is the value of mn?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer30)
If\[7\text{ }si{{n}^{2}}\theta +3\,\,co{{s}^{2}}\theta =4\], then which of the following is equal to tan \[\theta \]?
A)
1 done
clear
B)
\[\frac{\sqrt{3}}{2}\] done
clear
C)
\[\frac{1}{\sqrt{3}}\] done
clear
D)
\[\frac{1}{2}\] done
clear
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