Trigonometry SSC CGL-Quantitative Aptitude Question, Trigonometry CGL MCQ Question

1.

The value of

\[ \frac{\sin(23^\circ)\cos(67^\circ) + \sec(52^\circ)\sin(38^\circ) + \cos(23^\circ)\sin(67^\circ) + \operatorname{cosec}(52^\circ)\cos(38^\circ)} {\operatorname{cosec}^2(20^\circ) - \tan^2(70^\circ)} \]

is :
SSC CGL 2021-11.04.2022-1

A.

3

B.

4

C.

2

D.

0

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2.

If 4sin²θ = 3(1 + cosθ), 0° < θ < 90°, then what is the value of (2tanθ + 4sinθ - secθ)?
SSC CGL 2021-11.04.2022-1

A.

3\(\sqrt{15}\)- 4

B.

15\(\sqrt{3}\) - 4

C.

15\(\sqrt{3}\) + 3

D.

4\(\sqrt{15}\) - 3

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3.

The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?
SSC CGL 2021-11.04.2022-1

A.

78\(\sqrt{3}\)

B.

80

C.

52\(\sqrt{3}\)

D.

26\(\sqrt{3}\)

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4.

A vertical pole and a vertical tower are on the same level of ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the tower is 76 m, then find the height (in m) of the pole.
SSC CGL 2021-11.04.2022-2

A.

19\(\sqrt{3}\)

B.

57

C.

38

D.

19

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5.

What is the value of:
8 \(\sqrt{3}\) sin 30° tan 60° - 3 cos 0° + 3 sin² 45° + 2 cos² 30°?
SSC CGL 2021-11.04.2022-2

A.

18

B.

15

C.

9

D.

12

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6.

If cos(A - B) = \(\dfrac{\sqrt{3}}{2}\) and sec A = 2, 0° ≤ A ≤ 90°, 0° ≤ B ≤ 90°, then what is the measure of B?
SSC CGL 2021-11.04.2022-2

A.

60°

B.

0°

C.

30°

D.

90°

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Trigonometry SSC CGL Questions

Trigonometry MCQ Questions