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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 13 of 42 pages
Question 121. If sinα .sec(30° + α) = 1, (0 < α < 60°), then the value of sinα + cos2α is?
  1.    1
  2.    $$\frac{{2 + \sqrt 3 }}{{2\sqrt 3 }}$$
  3.    0
  4.    $$\sqrt 2 $$
 Discuss Question
Answer: Option A. -> 1
Question 122. The value of cotθ.tan(90° - θ) - sec(90° - θ)cosecθ + (sin225° + sin265°) + $$\sqrt 3 $$ (tan5°. tan15°. tan30°. tan75°. tan85°)
  1.    1
  2.    -1
  3.    2
  4.    0
 Discuss Question
Answer: Option A. -> 1
Question 123. If ∠A and ∠B are complementary to each other, then the value of sec2A + sec2B - sec2A.sec2B is?
  1.    1
  2.    -1
  3.    2
  4.    0
 Discuss Question
Answer: Option D. -> 0
Question 124. If A, B and C be the angles of a triangle, the incorrect relation is ?
  1.    $${\text{sin }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{cos}}\frac{{\text{C}}}{2}$$    
  2.    $${\text{cos }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = {\text{sin}}\frac{{\text{C}}}{2}$$    
  3.    $${\text{tan }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \sec \frac{{\text{C}}}{2}$$    
  4.    $${\text{cot }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \tan \frac{{\text{C}}}{2}$$    
 Discuss Question
Answer: Option C. -> $${\text{tan }}\left( {\frac{{{\text{A + B}}}}{2}} \right) = \sec \frac{{\text{C}}}{2}$$    
Question 125. If cosθ.cosec23° = 1, the value of θ is?
  1.    23°
  2.    37°
  3.    63°
  4.    67°
 Discuss Question
Answer: Option D. -> 67°
Question 126. If $$\theta $$ is a positive acute angle and $$\tan 2\theta .\tan 3\theta $$    = 1 then the value of $$\left( {{\text{2co}}{{\text{s}}^2}\frac{{5\theta }}{2} - 1} \right)$$   is?
  1.    $$ - \frac{1}{2}$$
  2.    1
  3.    0
  4.    $$\frac{1}{2}$$
 Discuss Question
Answer: Option C. -> 0
Question 127. If tan7θ.tan2θ = 1, then the value of tan3θ is?
  1.    $$\sqrt 3 $$
  2.    $$ - \frac{1}{{\sqrt 3 }}$$
  3.    $$\frac{1}{{\sqrt 3 }}$$
  4.    $$ - \sqrt 3 $$
 Discuss Question
Answer: Option C. -> $$\frac{1}{{\sqrt 3 }}$$
Question 128. If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$   = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$   then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$   is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta < {60^ \circ }$$ and $$\psi > {30^ \circ }$$  ) ?
  1.    $$\frac{1}{{\sqrt 3 }}$$
  2.    0
  3.    $$\sqrt 3 $$
  4.    1
 Discuss Question
Answer: Option C. -> $$\sqrt 3 $$
Question 129. Evaluate : 3cos80°.cosec10° + 2cos59°.cosec31°
  1.    1
  2.    3
  3.    2
  4.    5
 Discuss Question
Answer: Option D. -> 5
Question 130. $$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$   $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$   $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$         is equal to?
  1.    -1
  2.    0
  3.    1
  4.    2
 Discuss Question
Answer: Option C. -> 1

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