10th Class Mathematics Introduction to Trigonometry Question Bank

done MCQs - Introduction to Trigonometry Total Questions - 45

• question_answer1)
  Trigonometry is branch of Mathematics in which we deal with the relationship between angle and sides of a triangle.
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially True/False done clear
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• question_answer2)
  If \[\cos \,A=\frac{4}{5}\], then the value of tan A is
  A)
  3/5 done clear
  B)
  3/4 done clear
  C)
  4/3 done clear
  D)
  5/3 done clear
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• question_answer3)
  If \[\sin \theta =\frac{a}{b}\], then \[\cos \theta \] is equal to
  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
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• question_answer4)
  If \[\cos \theta =\frac{2}{3}\], then the value of \[2{{\sec }^{2}}\theta +2{{\tan }^{2}}\theta -9\] is
  A)
  2 done clear
  B)
  -2 done clear
  C)
  1 done clear
  D)
  3 done clear
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• question_answer5)
  If \[x\,\cos \,A=8\]and \[15\,\cos ec\,A=8\,\sec \,A\], then the value of x is
  A)
  20 done clear
  B)
  16 done clear
  C)
  17 done clear
  D)
  13 done clear
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• question_answer6)
  If \[\alpha \,\sin A=5\] and \[7\,\cos ec\,A=6\,\sec \,A\], then the value of a is
  A)
  \[\frac{46}{45}\] done clear
  B)
  \[\frac{46}{7}\] done clear
  C)
  \[\frac{49}{46}\] done clear
  D)
  None of these done clear
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• question_answer7)
  If \[\theta \] is an acute angle and \[4\,\sin \theta =3\], then the value of \[4\,{{\sin }^{2}}\theta -3\,{{\cos }^{2}}\theta +2\]is
  A)
  \[\frac{45}{16}\] done clear
  B)
  \[\frac{35}{18}\] done clear
  C)
  \[\frac{32}{16}\] done clear
  D)
  \[\frac{47}{16}\] done clear
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• question_answer8)
  If \[\sin \,A=\frac{4}{5}\], then the value of \[\frac{1-\sin A}{1+\cos A}\]is
  A)
  \[\frac{1}{8}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  2 done clear
  D)
  \[\frac{3}{5}\] done clear
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• question_answer9)
  In \[\Delta PQR\], \[\angle Q=90{}^\circ \]. If PQ = 10 cm and PR =15 cm. Then, the value of \[{{\tan }^{2}}P+{{\sec }^{2}}P+1\]is
  A)
  \[\frac{5}{2}\] done clear
  B)
  \[\frac{3}{17}\] done clear
  C)
  \[\frac{9}{2}\] done clear
  D)
  \[\frac{4}{5}\] done clear
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• question_answer10)
  In \[\Delta ABC\], if\[AB=BC\], \[\angle B=90{}^\circ \], then the value sin A is
  A)
  \[\frac{1}{\sqrt{2}}\] done clear
  B)
  \[\frac{\sqrt{3}}{2}\] done clear
  C)
  0 done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer11)
   

  In \[\Delta ABC\], if\[AB=2BC\], \[\angle B=90{}^\circ \], then the value of sec A is

  A)
  \[\frac{1}{\sqrt{2}}\] done clear
  B)
  \[\frac{\sqrt{3}}{2}\] done clear
  C)
  \[\frac{\sqrt{5}}{2}\] done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer12)
  The value of \[\cos \theta \]increase as \[\theta \] increase.
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially True/False done clear
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• question_answer13)
  Is \[{{\tan }^{2}}30{}^\circ +{{\cot }^{2}}30{}^\circ =\frac{10}{3}?\]
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially True/False done clear
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• question_answer14)
  \[\sin \,2A=2\,\sin \,A\]is true when A is equal to
  A)
  \[0{}^\circ \] done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer15)
  \[{{\cot }^{2}}30{}^\circ +\cos ec30{}^\circ +3{{\tan }^{2}}30{}^\circ \]is equal to
  A)
  3 done clear
  B)
  1 done clear
  C)
  0 done clear
  D)
  6 done clear
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• question_answer16)
  The value of \[\frac{2\tan \,30{}^\circ }{1-{{\tan }^{2}}30{}^\circ }\]will be
  A)
  \[cos\,60{}^\circ \] done clear
  B)
  \[sin\text{ }60{}^\circ \] done clear
  C)
  \[tan\,60{}^\circ \] done clear
  D)
  \[cot\text{ }60{}^\circ \] done clear
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• question_answer17)
  If\[\tan \theta =\frac{1}{\tan \theta }=2\], then the value of \[\cos ec\,\theta \] is
  A)
  1 done clear
  B)
  \[\frac{1}{\sqrt{2}}\] done clear
  C)
  \[\sqrt{2}\] done clear
  D)
  \[\frac{\sqrt{3}}{2}\] done clear
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• question_answer18)
  If x\[\tan \,45{}^\circ \,cos\,60{}^\circ =\sin \,60{}^\circ \,\cot \,60{}^\circ \], then the value of x will be
  A)
  1 done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\frac{\sqrt{3}}{2}\] done clear
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• question_answer19)
  \[7\,\cos \,30{}^\circ +5\,\tan \,30{}^\circ +6\,\cot \,60{}^\circ \] is
  A)
  \[\frac{43}{2\sqrt{3}}\] done clear
  B)
  \[\frac{41\sqrt{3}}{2}\] done clear
  C)
  \[\frac{47}{2\sqrt{3}}\] done clear
  D)
  \[\frac{49\sqrt{3}}{2}\] done clear
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• question_answer20)
  If\[\tan \theta -\frac{4}{\tan \theta }=3\], then \[{{\sin }^{2}}\theta \]is
  A)
  \[\frac{4}{17}\] done clear
  B)
  \[\frac{3}{17}\] done clear
  C)
  \[\frac{16}{17}\] done clear
  D)
  \[\frac{5}{17}\] done clear
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• question_answer21)
  If \[\sin \alpha =\frac{1}{2}\] and \[\cos \beta =\frac{1}{2}\], then the value of \[\left( \alpha +\beta  \right)\] is
  A)
  \[60{}^\circ \] done clear
  B)
  \[90{}^\circ \] done clear
  C)
  \[30{}^\circ \] done clear
  D)
  \[45{}^\circ \] done clear
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• question_answer22)
  If \[\tan \,A=\frac{1}{\sqrt{3}}\]and \[\tan \,B=\sqrt{3}\], then \[\tan \,\left( A+B \right)\] is
  A)
  0 done clear
  B)
  \[\frac{1}{\sqrt{3}}\] done clear
  C)
  1 done clear
  D)
  \[\infty \] done clear
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• question_answer23)
  If\[\sqrt{3}\tan \theta =2\,\sin \theta \], then the value \[{{\sin }^{2}}\theta -{{\cos }^{2}}\theta \] is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[-\frac{1}{2}\] done clear
  C)
  \[\frac{3}{2}\] done clear
  D)
  \[\frac{-3}{2}\] done clear
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• question_answer24)
  If \[\sin \theta -\cos \theta =0\], then the value of \[{{\sin }^{4}}\theta +{{\cos }^{4}}\theta \] will be
  A)
  \[\frac{1}{4}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{3}{4}\] done clear
  D)
  1 done clear
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• question_answer25)
  If m \[\tan \,30{}^\circ \]\[\cot \,60{}^\circ =\sin \,45{}^\circ \]\[\cos 45{}^\circ \], then the value of m will be
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{3}{2}\] done clear
  C)
  \[\frac{1}{3}\] done clear
  D)
  \[\frac{3}{4}\] done clear
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• question_answer26)
  The value of \[\frac{2\tan \,30{}^\circ }{1+{{\tan }^{2}}30{}^\circ }\] is
  A)
  \[sin60{}^\circ \] done clear
  B)
  \[cos60{}^\circ \] done clear
  C)
  \[tan60{}^\circ \] done clear
  D)
  \[sin30{}^\circ \] done clear
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• question_answer27)
  The value of \[\frac{1-{{\tan }^{2}}45{}^\circ }{1+{{\tan }^{2}}45{}^\circ }\] is
  A)
  \[tan90{}^\circ \] done clear
  B)
  1 done clear
  C)
  \[sin45{}^\circ \] done clear
  D)
  0 done clear
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• question_answer28)
  The value of \[\frac{\tan \,30{}^\circ }{\cot \,60{}^\circ }\]is
  A)
  1 done clear
  B)
  -1 done clear
  C)
  2 done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer29)
  If A, B, C are the angles of a \[\Delta ABC\], then the value of \[\tan \,\left( \frac{B+C}{2} \right)\]is
  A)
  \[\cot \,\frac{B}{2}\] done clear
  B)
  \[\tan \,\frac{A}{2}\] done clear
  C)
  \[\cot \,\frac{C}{2}\] done clear
  D)
  \[\cot \,\frac{A}{2}\] done clear
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• question_answer30)
  If \[\cos \,A+{{\cos }^{2}}A=1\], then the value of \[{{\sin }^{2}}A+{{\sin }^{4}}A\]is
  A)
  0 done clear
  B)
  1 done clear
  C)
  -1 done clear
  D)
  2 done clear
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• question_answer31)
  Is \[\sin \left( A+B \right)=\sin A+\sin \,B\]?
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially True/False done clear
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• question_answer32)
  Is \[\frac{1-\sin \theta }{1+\sin \theta }={{\sec }^{2}}\theta -{{\tan }^{2}}\theta \]?
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially True/False done clear
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• question_answer33)
  The value of \[\frac{1+{{\tan }^{2}}A}{1+{{\cot }^{2}}A}\] is
  A)
  \[{{\sec }^{2}}A\] done clear
  B)
  -1 done clear
  C)
  \[{{\cot }^{2}}A\] done clear
  D)
  \[{{\tan }^{2}}A\] done clear
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• question_answer34)
  The value of \[\left( 1+\tan \theta +\sec \theta  \right)\] \[\left( 1+\cot \theta -\cos ec\theta  \right)\] is
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  -1 done clear
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• question_answer35)
  If \[4x=\cos ec\theta \]and \[\frac{4}{x}=\cot \theta \], then the value of \[4\left[ {{x}^{2}}-\frac{1}{{{x}^{2}}} \right]\]is
  A)
  \[\frac{1}{4}\] done clear
  B)
  4 done clear
  C)
  2 done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer36)
  The value of \[\frac{\sin \theta \,\tan \theta }{1-\cos \,\theta }+{{\tan }^{2}}\theta -{{\sec }^{2}}\theta \] is
  A)
  \[\sin \theta \,\cos \theta \] done clear
  B)
  \[\sec \theta \] done clear
  C)
  \[\tan \theta \] done clear
  D)
  \[\cos ec\theta \] done clear
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• question_answer37)
  If\[\sec \theta =x+\frac{1}{4x}\], then the value of \[\sec \theta +\tan \theta \] is
  A)
  4x done clear
  B)
  2x done clear
  C)
  x done clear
  D)
  \[\frac{x}{2}\] done clear
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• question_answer38)
  If \[\sqrt{3}{{\cot }^{2}}\theta -4\,\cot \theta +\sqrt{3}=0\], then the value of  \[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta \] is
  A)
  \[\frac{3}{10}\] done clear
  B)
  \[\frac{-10}{3}\] done clear
  C)
  \[\frac{10}{3}\] done clear
  D)
  \[\frac{-20}{3}\] done clear
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• question_answer39)
  If \[\tan \theta +sec\theta =l\], then the value of \[\sec \theta \] is
  A)
  \[\frac{{{l}^{2}}-1}{2l}\] done clear
  B)
  \[\frac{{{l}^{2}}+1}{2l}\] done clear
  C)
  \[\frac{{{l}^{2}}-1}{l}\] done clear
  D)
  \[\frac{2\left( {{l}^{2}}-1 \right)}{l}\] done clear
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• question_answer40)
  If \[\tan \,A=a\,\tan \,B\] and \[\sin \,A=b\,\sin \,B\],  then the value of \[{{\cos }^{2}}A\]is
  A)
  \[\frac{{{a}^{2}}-1}{{{b}^{2}}-1}\] done clear
  B)
  \[\frac{{{a}^{2}}+1}{{{b}^{2}}-1}\] done clear
  C)
  \[\frac{{{b}^{2}}-1}{{{a}^{2}}+1}\] done clear
  D)
  \[\frac{{{b}^{2}}-1}{{{a}^{2}}-1}\] done clear
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• question_answer41)
  If \[\cos ec\,A=\cot \,a=q\], then the value of \[\frac{{{q}^{2}}-1}{{{q}^{2}}+1}+\cos \,A\] is
  A)
  1 done clear
  B)
  0 done clear
  C)
  -1 done clear
  D)
  2 done clear
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• question_answer42)
  If \[x=r\] \[\sin A\,\operatorname{cosB}\], \[y=r\] \[\sin \,A\,\sin \,B\]and \[z=r\,\cos \,A\], then the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] is
  A)
  \[\frac{{{r}^{2}}}{2}\] done clear
  B)
  \[{{r}^{2}}\] done clear
  C)
  \[{{r}^{2}}-1\] done clear
  D)
  \[{{r}^{2}}+1\] done clear
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• question_answer43)
  If \[{{\sin }^{2}}A=1\], then the value of\[{{\sin }^{2}}A-{{\cos }^{2}}A\]is
  A)
  1 done clear
  B)
  0 done clear
  C)
  2 done clear
  D)
  None of these done clear
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• question_answer44)
  Match the following.

  	Column - I		Column- II
  P.	\[\frac{\sin \,0{}^\circ }{\cos 90{}^\circ }+\sin \,45{}^\circ \]	1.	\[\left( \frac{1-\sqrt{3}}{2} \right)\]
  Q.	\[\cos \,60{}^\circ -\sin \,60{}^\circ \]	2.	\[1+\frac{\sqrt{2}}{3}\]
  R.	\[\sec 30{}^\circ \sin 60{}^\circ \] \[+\cos 45{}^\circ \cos ec\,60{}^\circ \]	3.	1
  S.	\[\frac{{{\cos }^{3}}30{}^\circ -{{\cos }^{3}}60{}^\circ }{{{\sin }^{3}}60{}^\circ -{{\sin }^{3}}30{}^\circ }\]	4.	\[\frac{1}{\sqrt{2}}\]

  A)
  P-2,      Q-4,      R-3,      S-1 done clear
  B)
  P-3,      Q-1,      R-4,      S-1 done clear
  C)
  P-2,      Q-3,      R-4,      S-1 done clear
  D)
  P-4,      Q-1,      R-2,      S-3 done clear
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• question_answer45)
  Match the following.

  	Column - I		Column - II
  P.	\[1+\frac{{{\cot }^{2}}\theta }{1+\cos ec\theta }\]	1.	\[2\tan \theta \]
  Q.	\[\frac{\cos \theta }{\cos ec\theta +1}\] \[+\frac{\cos \theta }{\cos ec\theta -1}\]	2.	\[{{\left( \frac{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }{\cos \theta \,\sin \theta } \right)}^{2}}\]
  R.	\[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta -2\]	3.	\[{{\left( \cos ec\theta -\cot \theta  \right)}^{2}}\]
  S.	\[\frac{1-\cos \theta }{1+\cos \theta }\]	4.	\[\sec \theta \cot \theta \]

  A)
  P-3,      Q-4,      R-2,      S-1 done clear
  B)
  P-3,      Q-1,      R-4,      S-2 done clear
  C)
  P-2,      Q-3,      R-4,      S-1 done clear
  D)
  P-4,      Q-1,      R-2,      S-3 done clear
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