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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 5 of 42 pages
Question 41. If $$\sec \theta - \tan \theta = \frac{1}{{\sqrt 3 }}{\text{,}}$$    the value of $$\sec \theta $$ . $$\tan \theta $$  = ?
  1.    $$\frac{4}{{\sqrt 3 }}$$
  2.    $$\frac{2}{{\sqrt 3 }}$$
  3.    $$\frac{2}{3}$$
  4.    $$\frac{1}{{\sqrt 3 }}$$
 Discuss Question
Answer: Option C. -> $$\frac{2}{3}$$
Question 42. The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?
  1.    4
  2.    6
  3.    2
  4.    1
 Discuss Question
Answer: Option D. -> 1
Question 43. The value of θ(0 ≤ θ ≤ 90°) satisfying 2sin2θ = 3cosθ is?
  1.    60°
  2.    90°
  3.    30°
  4.    45°
 Discuss Question
Answer: Option A. -> 60°
Question 44. A, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a2 + b2 + c2 = ab + bc + ca, then the value of (sin2A + sin2B + sin2C) is?
  1.    $$\frac{3}{4}$$
  2.    $$\frac{3}{2}$$
  3.    $$\frac{{3\sqrt 3 }}{2}$$
  4.    $$\frac{9}{4}$$
 Discuss Question
Answer: Option D. -> $$\frac{9}{4}$$
Question 45. If $${\text{tan }}\alpha = 2,$$   then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}\alpha - {\text{se}}{{\text{c}}^2}\alpha }}{{{\text{cose}}{{\text{c}}^2}\alpha + se{c^2}\alpha }}$$   is?
  1.    $$ - \frac{5}{9}$$
  2.    $$\frac{3}{5}$$
  3.    $$ - \frac{3}{5}$$
  4.    $$\frac{{17}}{5}$$
 Discuss Question
Answer: Option C. -> $$ - \frac{3}{5}$$
Question 46. If $$\sin \left( {\theta + {{30}^ \circ }} \right) = \frac{3}{{\sqrt {12} }}{\text{,}}$$     then find $${\text{co}}{{\text{s}}^2}\theta ?$$
  1.    $$\frac{1}{4}$$
  2.    $$\frac{3}{4}$$
  3.    $$\frac{{\sqrt 3 }}{2}$$
  4.    $$\frac{1}{2}$$
 Discuss Question
Answer: Option B. -> $$\frac{3}{4}$$
Question 47. If $${\text{0}} \leqslant \theta \leqslant {90^ \circ }$$   and $$4{\cos ^2}\theta $$   - $$4\sqrt 3 \cos \theta $$   + 3 = 0 then the value of $$\theta $$ is?
  1.    30°
  2.    90°
  3.    45°
  4.    60°
 Discuss Question
Answer: Option A. -> 30°
Question 48. The value of sec4A(1 - sin4A) - 2tan2A is?
  1.    $$\frac{1}{2}$$
  2.    0
  3.    2
  4.    1
 Discuss Question
Answer: Option D. -> 1
Question 49. If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3}{\text{,}}$$     then the value of $${\text{2co}}{{\text{s}}^2}\theta - 1$$   is?
  1.    0
  2.    1
  3.    $$\frac{2}{3}$$
  4.    $$\frac{3}{2}$$
 Discuss Question
Answer: Option C. -> $$\frac{2}{3}$$
Question 50. If $$\sin \theta - \cos \theta = \frac{7}{{13}}$$    and $${0^ \circ }{\text{ < }}\theta {\text{ < }}{90^ \circ }{\text{,}}$$   then the value of $$\sin \theta $$  + $${\text{cos}}\theta $$  is?
  1.    $$\frac{{17}}{{13}}$$
  2.    $$\frac{{13}}{{17}}$$
  3.    $$\frac{1}{{13}}$$
  4.    $$\frac{1}{{17}}$$
 Discuss Question
Answer: Option A. -> $$\frac{{17}}{{13}}$$

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