71)

For what value of θ (in degrees) is the following equation true?
\( sin 3θ cos θ - cos 3θ sin θ ={1\over2}\), \(0<\theta<{\pi\over2}\)

, Avg: 01:11 , 33%✓ SSC CHSL 2021

A)

45

B)

60

C)

15

D)

30

72)

The value of \( \frac{cos 8^\circ \ cos 24^\circ \ cos 60^\circ \cos 66^\circ \ cos 82^\circ}{sin 82^\circ sin 66^\circ \ sin 60^\circ \ sin 8^\circ \ sin 24^\circ}\) is:

, Avg: 00:59 , 75%✓ SSC CHSL 2021

A)

\(\frac{1}{\sqrt{3}}\)

B)

1

C)

0

D)

\(\frac{1}{\sqrt{2}}\)

73)

If \( sin B =\frac{9}{41}\) , then what is the value of cot B, where 0° < B < 90°?

, Avg: 00:41 , 100%✓ SSC CHSL 2021

A)

\(\frac{41}{9}\)

B)

\(\frac{40}{9}\)

C)

\(\frac{9}{40}\)

D)

\(\frac{9}{41}\)

74)

If \(tan\theta ={4\over3}\), then the value of \(\frac{9\sin \theta+12\cos \theta}{27\cos \theta-20\sin \theta} \) will be equal to:

, Avg: 00:46 , 66%✓ SSC CHSL 2021

A)

72

B)

36

C)

100

D)

18

75)

Evaluate the following expression.
\( \frac{3(\cot^2 46^{\circ}-\sec^2 44^{\circ})}{2(\sin^2 28^{\circ}+\sin^2 62^{\circ})}+\)\(\frac{2\cos^2 60^{\circ}\tan^2 33^{\circ}\tan^2 57^{\circ}}{\sec^2(90^0-\theta)-\cot^2 \theta}\)

, Avg: 00:58 , 50%✓ SSC CHSL 2021

A)

1

B)

2

C)

-2

D)

-1

76)

For θ : 0° < θ < 90°
3 sec θ + 4 cos θ = 4√3, find the value of (1 - sin θ + cos θ).

, Avg: 01:46 , 100%✓ SSC CHSL 2021

A)

\(\frac{1-2\sqrt3}{2}\)

B)

\(\frac{1+\sqrt3}{2}\)

C)

\(\frac{1+2\sqrt3}{2}\)

D)

\(\frac{1-\sqrt3}{2}\)

77)

If sin² x - 3cos² x = 0, then the value of x (0 < x < 90°) is:

, Avg: 00:47 , 75%✓ SSC CHSL 2021

A)

45

B)

60

C)

15

D)

30

78)

If \({5cot\theta+\sqrt3cosec\theta\over 2\sqrt3coesec\theta+3 cot\theta}=1\), \(0^0<\theta<90^0\), then the value of \(\frac{\frac{7}{2} \cot^2 \theta- \frac{3}{4} \:cosec^2 \theta}{4 \sin^2 \theta+\frac{3}{2} \tan^2 \theta}\) will be:

, Avg: 00:13 , 33%✓ SSC CHSL 2021

A)

2

B)

7

C)

5

D)

3

79)

The value of \(\sqrt{\cos 60^{\circ} \cos 30^{\circ}- \sin60^{\circ} \sin 30^{\circ}}\) is:

, Avg: 00:27 , 75%✓ SSC CHSL 2021

A)

1

B)

\(\frac{1}{\sqrt2}\)

C)

0

D)

\(\frac{\sqrt3}{2}\)

80)

If (1 + cot²θ) + (1 +(cot²θ)^-1) is equal to k, then √k = ?

, Avg: 01:09 , 75%✓ SSC CHSL 2021

A)

sin θ sec θ

B)

sin θ cos θ

C)

cosec θ sec θ

D)

cosec θ cos θ