151)

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

SSC CHSL 2021

A)

sin θ sec θ

B)

sin θ cos θ

C)

cosec θ sec θ

D)

cosec θ cos θ

152)

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

SSC CHSL 2021

A)

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

B)

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

C)

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

D)

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

153)

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

SSC CHSL 2021

A)

22.5

B)

21.5

C)

23.5

D)

20.5

154)

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

SSC CHSL 2021

A)

0

B)

1

C)

∞

D)

not defined

155)

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

SSC CHSL 2021

A)

secθ cosecθ

B)

cosθ cosecθ

C)

secθ sinθ

D)

sinθ cosθ

156)

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

SSC CHSL 2021

A)

0

B)

2

C)

1

D)

3

157)

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

SSC CHSL 2021

A)

2

B)

5

C)

3

D)

1

158)

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

SSC CHSL 2021

A)

15°

B)

60°

C)

45°

D)

30°

159)

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:

SSC CHSL 2021

A)

8

B)

4

C)

6

D)

3

160)

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

SSC CHSL 2021

A)

0

B)

1

C)

3/2

D)

1/2