81)

If 3 cos θ = 2 sin² θ, \(0^0<\theta<90^0\), then what is the value of (tan² θ + sec² θ - cosec² θ)?

, Avg: 01:18 , 100%✓ SSC CHSL 2021

A)

\(\frac{17}{3}\)

B)

\(-\frac{7}{3}\)

C)

\(-\frac{17}{3}\)

D)

\(\frac{7}{3}\)

82)

The value of cot²46° - sec²44° + (sin²1° + sin ²3° + sin²5° + ....+ sin²89°) is:

, Avg: 01:26 , 66%✓ SSC CHSL 2021

A)

22.5

B)

21.5

C)

23.5

D)

20.5

83)

If 3 sin² A + 4 cos² A - 3 = 0, then the value of cot A (where 0 ≤ A ≤ 90°) is:

, Avg: 01:14 , 33%✓ SSC CHSL 2021

A)

0

B)

1

C)

∞

D)

not defined

84)

The value of \(\frac{\sec \theta \ cosec \theta}{2+\tan^2 \theta+\cot^2 \theta}\) is equal to:

, Avg: 01:25 , 66%✓ SSC CHSL 2021

A)

secθ cosecθ

B)

cosθ cosecθ

C)

secθ sinθ

D)

sinθ cosθ

85)

The value of \([\frac{\sin^227^{\circ}+\sin^263^{\circ}}{\cos^224^{\circ}+\cos^266^{\circ}}\)\(-\sin^269^{\circ}-\)\(\cos69^{\circ}\sin21^{\circ}]\) is:

, Avg: 00:42 , 100%✓ SSC CHSL 2021

A)

0

B)

2

C)

1

D)

3

86)

If cot² θ + cot⁴ θ = 2, then the value of 2 sin⁴ θ + sin² θ is:

, Avg: 00:37 , 75%✓ SSC CHSL 2021

A)

2

B)

5

C)

3

D)

1

87)

Solve for θ : 3 cosec θ + 4 sin θ - 4√3 = 0, where θ is an acute angle.

, Avg: 01:03 , 60%✓ SSC CHSL 2021

A)

15°

B)

60°

C)

45°

D)

30°

88)

If cot A + cosec A = 2 and A is an acute angle, then the value of \(\frac{9\tan A+16\ cosec\ A}{5\sin A+3\tan A} \) is:

, Avg: 01:20 , 100%✓ SSC CHSL 2021

A)

8

B)

4

C)

6

D)

3

89)

If \(sin α + csc α = tan{\pi\over 3}\), then the value of (sin³α + csc³α) is equal to:

, Avg: 01:01 , 50%✓ SSC CHSL 2021

A)

0

B)

1

C)

3/2

D)

1/2

90)

If 6tan² α - 2 = 0, (0 < α < 90°), then the value of α is:

, Avg: 00:14 , 100%✓ SSC CHSL 2021

A)

75°

B)

15°

C)

45°

D)

30°