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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 2 of 42 pages
Question 11. If α + β = 90°, then the value of (1 - sin2α)(1 - cos2α) × (1 + cot2β)(1 + tan2β) is?
  1.    1
  2.    -1
  3.    0
  4.    2
 Discuss Question
Answer: Option A. -> 1
Question 12. If $${\text{tan }}{9^ \circ } = \frac{p}{q}{\text{,}}$$   then the value of $$\frac{{{\text{se}}{{\text{c}}^2}{\text{8}}{{\text{1}}^ \circ }}}{{1 + {{\cot }^2}{{81}^ \circ }}}$$   is?
  1.    $$\frac{p}{q}$$
  2.    1
  3.    $$\frac{{{p^2}}}{{{q^2}}}$$
  4.    $$\frac{{{q^2}}}{{{p^2}}}$$
 Discuss Question
Answer: Option D. -> $$\frac{{{q^2}}}{{{p^2}}}$$
Question 13. If 7sin2θ + 3cos2θ = 4, (0° ≤ θ ≤ 90°), then the value of θ is?
  1.    $$\frac{\pi }{2}$$
  2.    $$\frac{\pi }{3}$$
  3.    $$\frac{\pi }{6}$$
  4.    $$\frac{\pi }{4}$$
 Discuss Question
Answer: Option C. -> $$\frac{\pi }{6}$$
Question 14. The value of following is, cos24° + cos55° + cos125° + cos204° + cos300° ?
  1.    $$ - \frac{1}{2}$$
  2.    $$\frac{1}{2}$$
  3.    2
  4.    1
 Discuss Question
Answer: Option B. -> $$\frac{1}{2}$$
Question 15. If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?
  1.    5°
  2.    9°
  3.    12°
  4.    15°
 Discuss Question
Answer: Option B. ->
Question 16. In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?
  1.    $$\frac{\pi }{6}$$
  2.    $$\frac{\pi }{{12}}$$
  3.    $$\frac{\pi }{4}$$
  4.    $$\frac{\pi }{2}$$
 Discuss Question
Answer: Option B. -> $$\frac{\pi }{{12}}$$
Question 17. If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?
  1.    $$ - \sqrt 3 $$
  2.    $$\frac{1}{{\sqrt 3 }}$$
  3.    1
  4.    $$\sqrt 3 $$
 Discuss Question
Answer: Option D. -> $$\sqrt 3 $$
Question 18. Sin2θ - 3sinθ +2 = 0, will be true if ?
  1.    0 ≤ θ ≤ 90°
  2.    0 < θ < 90°
  3.    θ = 0°
  4.    θ = 90°
 Discuss Question
Answer: Option D. -> θ = 90°
Question 19. If $$\sin \alpha + \cos \beta = 2;$$   $$\left( {{0^ \circ } \leqslant \beta < \alpha \leqslant {{90}^ \circ }} \right){\text{,}}$$     then $${\text{sin}}\,{\left( {\frac{{2\alpha + \beta }}{3}} \right)^ \circ }$$   is?
  1.    $${\text{sin }}\frac{\alpha }{2}$$
  2.    $$\cos \frac{\alpha }{3}$$
  3.    $${\text{sin }}\frac{\alpha }{3}$$
  4.    $$\cos \frac{{2\alpha }}{3}$$
 Discuss Question
Answer: Option B. -> $$\cos \frac{\alpha }{3}$$
Question 20. If $$2\sin \left( {\frac{{\pi x}}{2}} \right) = {x^2} + \frac{1}{{{x^2}}}{\text{,}}$$     then the value of $$\left( {x - \frac{1}{x}} \right)$$   is?
  1.    -1
  2.    2
  3.    1
  4.    0
 Discuss Question
Answer: Option D. -> 0

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