131)

In a triangle ABC, right-angled at C, if \(sec A={13\over5}\), then find the value of \(\frac{1+ \sin A}{\cos B}\).

SSC CHSL 2021

A)

\(\frac{3}{2}\)

B)

5

C)

\(\frac{25}{12}\)

D)

\(\frac{18}{5}\)

132)

If sinθ + cosecθ = 7, then what is the value of sin³θ + cosec³θ?

SSC CHSL 2021

A)

382

B)

350

C)

322

D)

367

133)

If \({sin^2\theta\over tan^2\theta-sin^2\theta}=5\), then the value of \(\frac{24\cos^2\theta-15\sec^2\theta}{6\ \rm cosec^2 \theta-7\cot^2\theta}\) is:

SSC CHSL 2021

A)

1

B)

6

C)

2

D)

4

134)

If 3 cot A = 4 tan A and A is an acute angle, then what will be the value of sec A ?

SSC CHSL 2021

A)

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

B)

\(\frac{\sqrt7}{2}\)

C)

\(\frac{\sqrt{21}}{3}\)

D)

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

135)

What is the value of \(\frac{\cos^2 20^{\circ}+\cos^2 70^{\circ}}{\sin^2 90^{\circ}}\)\(-\tan^2 45^{\circ}\) ?

SSC CHSL 2021

A)

-2

B)

-1

C)

0

D)

1

136)

If √13 sin θ = 2, then the value of \(\frac{3\tan \theta+\sqrt{13} \sin\theta}{\sqrt{13} \cos \theta - 3\tan \theta}\) is:

SSC CHSL 2021

A)

3

B)

4

C)

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

D)

5

137)

If cos²θ -  sin²θ - 3 cos θ + 2 = 0, \(0^0<\theta<90^0\), then what will be the value of sec θ - cos θ?

SSC CHSL 2021

A)

\(\frac{2}{3}\)

B)

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

C)

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

D)

\(\frac{3}{2}\)

138)

If \(\frac{\cot \theta + \cos \theta}{\cot \theta - \cos \theta}\) \(=\frac{k+1}{1-k}\), \(k \ne 1\), then k is equal to:

SSC CHSL 2021

A)

cosθ

B)

cosecθ

C)

sinθ

D)

secθ

139)

If 5 cos θ = 4 sin θ, 0° ≤ θ ≤ 90°, then what will be the value of sec θ?

SSC CHSL 2021

A)

\(\frac{\sqrt{41}}{16}\)

B)

\(\frac{\sqrt{41}}{4}\)

C)

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

D)

\(\frac{\sqrt{41}}{5}\)

140)

If \({cosec^2\theta\over cosec^2\theta-cot^2\theta}={13\over4}\), \(0^0<\theta<90^0\), then the value of \(\frac{52 \cos^2 \theta-9 \tan^2 \theta}{18 \sec^2 \theta + 8 \cot^2 \theta}\) will be:

SSC CHSL 2021

A)

\(\frac{5}{11}\)

B)

\(\frac{4}{11}\)

C)

\(\frac{8}{13}\)

D)

\(\frac{8}{11}\)