10th Class Mathematics Introduction to Trigonometry Question Bank

done Trigonometry Total Questions - 30

• 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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