31)

Simplify the following expression:
cosec⁴ A(1 - cos⁴ A) - 2 cot² A - 1

SSC CGL 2022

A)

sin² A

B)

0

C)

cosec² A

D)

1

32)

If 6tanA (tanA + 1) = 5 - tanA, Given that  \( 0 < A< \frac{\pi}{2}\) what is the value of (sinA + cosA)?

SSC CGL 2022

A)

\(\frac{5}{{\sqrt 3 }}\)

B)

\(5 \sqrt{3}\)

C)

\(3 \sqrt{5}\)

D)

\(\frac{3}{{\sqrt 5 }}\)

33)

If tan B =5/3, then what is the value of \( cosec B +sin B \over cos B - secB\) ?

SSC CGL 2022

A)

\(59\over15\)

B)

\(177\over 125\)

C)

\(- {177\over125}\)

D)

\(-{59\over15}\)

34)

If tan² A - 6 tan A + 9 = 0, 0 < A < 90°, what is the value of \(6 cot A + 8 \sqrt{10} cos A\)?

SSC CGL 2022

A)

14

B)

10 \(\sqrt{10}\)

C)

8 \(\sqrt{10}\)

D)

10

35)

The value of \(\left(\frac{1-\cot θ}{1-\tan θ}\right)^{2} + 1\), if 0° < θ < 90°, is equal to:

SSC CGL 2022

A)

sec²θ

B)

sin²θ

C)

cosec²θ

D)

cos²θ

36)

The value of \(\frac{5 \cos ^{2} 62^{\circ}+5 \cos ^{2} 28^{\circ}-21}{7 \sin ^{2} 35^{\circ}+7 \sin ^{2} 55^{\circ}+1}\) is:

SSC CGL 2022

A)

2

B)

3

C)

-2

D)

-3

37)

If A = 30°, what is the value of: \(\frac{\left[8 \sin \mathrm{A}+11 \operatorname{cosec} \mathrm{A}-\cot ^{2} \mathrm{A}\right]}{10 \cos 2 \mathrm{A}}\) ?

SSC CGL 2022

A)

\(5 \frac{1}{5}\)

B)

\(4 \frac{2}{5}\)

C)

\(3 \frac{4}{5}\)

D)

\(4 \frac{3}{5}\)

38)

If (2 cos A + 1) (2 cos A - 1) = 0, 0° < A ≤ 90°, then find the value of A.

SSC CGL 2022

A)

90°

B)

45°

C)

60°

D)

30°

39)

If \(tan A = \frac{{2.4}}{{0.7}}\) ,what is the value of (50 cos A + 24 cot A)?

SSC CGL 2022

A)

37

B)

21

C)

26

D)

34

40)

If sec² α + 4 cos²α = 4 and 0° ≤ α ≤ 90°, then find the value of α.

SSC CGL 2022

A)

0°

B)

60°

C)

30°

D)

45°