191)

If cot B = \(\frac{12}{5}\) , what is the value of sec B?

SSC CGL 2022

A)

\(\frac{13}{5}\)

B)

\(\frac{5}{12}\)

C)

\(\frac{13}{12}\)

D)

\(\frac{12}{13}\)

192)

The value of \(1 + \sqrt { {\cotθ + \cosθ} \over \cotθ - \cosθ}\) , if 0° < θ < 90°, is equal to:

SSC CGL 2022

A)

1 + sec θ − tan θ

B)

1 − sec θ − tan θ

C)

1 − sec θ + tan θ

D)

1 + sec θ + tan θ

193)

The value of \( \left({ {1 - \cotθ} \over 1 - \tanθ}\right)^2 - 1\) when 0° < θ < 90°, is equal to:

SSC CGL 2022

A)

cot² θ - 1

B)

sec² θ + 1

C)

cos² - 1

D)

sin² θ - 1

194)

tan² A + 5 sec A = 13, where 0 < A < 90°. Solve for A (in degrees).

SSC CGL 2022

A)

45

B)

60

C)

0

D)

30

195)

If 2k sin 30° cos 30° cot 60° = \(\frac{{{{\cot }^2}30^\circ \sec 60^\circ \tan 45^\circ }}{{{\rm{cose}}{{\rm{c}}^{\rm{2}}}{\rm{45^\circ cosec 30}}^\circ }}\) , then find the value of k.

SSC CGL 2022

A)

1

B)

3

C)

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

D)

6

196)

Find the value of the following expression:
\( \frac{{{{\tan }^3}45^\circ + 4{{\cos }^3}60^\circ }}{{2{\rm{cose}}{{\rm{c}}^2}45^\circ - 3{{\sec }^2}30^\circ + \sin 30^\circ }}\)

SSC CGL 2022

A)

\(1 + \sqrt 2\)

B)

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

C)

3

D)

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

197)

If 5 sin θ - 4 cos θ = 0, 0° < θ < 90°, then the value of \(\frac{{{\rm{5sin}}\,{\rm{\theta }}\,{\rm{ + }}\,{\rm{2 cos}}\,{\rm{\theta }}}}{{{\rm{5sin}}\,{\rm{\theta }}\,{\rm{ + }}\,{\rm{3 cos}}\,{\rm{\theta }}}}\) is:

SSC CGL 2022

A)

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

B)

\(\frac{4}{7}\)

C)

\(\frac{6}{7}\)

D)

\(\frac{2}{7}\)

198)

If 5 sin θ – 4 cos θ = 0, 0° < θ < 90°, then the value of \(\frac{5sin\theta-cos\theta}{5sin\theta+3cos\theta}\) is:

SSC CGL 2022

A)

\(\frac{2}{7}\)

B)

\(\frac{4}{7}\)

C)

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

D)

\(\frac{6}{7}\)

199)

The expression (cos⁶ θ + sin⁶ θ – 1)(tan² θ + cot² θ + 2) + 3 is equal to:

SSC CGL 2022

A)

1

B)

2

C)

0

D)

–1

200)

If sin²θ - cos²θ - 3sinθ + 2 = 0, 0° < θ < 90°, then what is the value of 1 + secθ + tanθ?

SSC CGL 2022

A)

-1 + √3

B)

1 + √3

C)

-1 - √3

D)

1 - √3