171)

If \(tan A + sec A ={3\over2}\) and A is an acute angle, then the value of \( \frac{10\cot A+13\cos A}{12 \tan A + 5 \ cosec \ A} \) is:

SSC CHSL 2021

A)

2

B)

5

C)

4

D)

1

172)

If 4 – 2sin² θ – 5cos θ = 0, 0° < θ < 90°, then the value of cos θ + tan θ is :

SSC CPO 2020

A)

\(\dfrac{1-2\sqrt{3}}{2}\)

B)

\(\dfrac{2-\sqrt{3}}{2}\)

C)

\(\dfrac{1+2\sqrt{3}}{2}\)

D)

\(\dfrac{2+\sqrt{3}}{2}\)

173)

If 4(cosec² 57° - tan² 33°) - cos 90° - y tan² 66° tan² 24° =\(\dfrac{y}{2}\) , the value of y is:

SSC CPO 2020

A)

\(\dfrac{1}{3}\)

B)

\(\dfrac{8}{3}\)

C)

8

D)

\(\dfrac{3}{8}\)

174)

The value of \(\frac {\sin^2 30^\circ + \cos^2 60^\circ - \sec 35^\circ.\sin 55^\circ}{\sec 60^\circ + \rm cosec\;30^\circ} \) is equal to:

SSC CPO 2020

A)

\(\frac 1 4\)

B)

\(-\frac 1 4\)

C)

\(\frac 1 8\)

D)

\(-\frac 1 8\)

175)

If sec3x = cosec(3x - 45°), where 3x is an acute angle, then x is equal to:

SSC CPO 2020

A)

35°

B)

45°

C)

22.5°

D)

27.5°

176)

The value of \(\frac{{{{\sin }^2}30^\circ + {{\cos }^2}60^\circ + sec45^\circ .sin45^\circ }}{{sec60^\circ + cosec30^\circ }} \) is:

SSC CPO 2020

A)

\(\frac{1}{4}\)

B)

\(\frac{3}{8}\)

C)

\(-\frac{1}{4}\)

D)

\(-\frac{3}{8}\)

177)

If sin3x = cos(3x – 45°), 0° < 3x < 90°, then x is equal to:

SSC CPO 2020

A)

27.5°

B)

45°

C)

35°

D)

22.5°

178)

If 4θ is an acute angle, and cot 4θ = tan (θ - 5°) , then what is the value of θ?

SSC CPO 2020

A)

24°

B)

45°

C)

21°

D)

19°

179)

The value of \(\frac{{{{\sin }^2}{}52^\circ + 2 + {{\sin }^2}{{ }}38^\circ }}{{4{}{{\cos }^2}43^\circ - 5 + 4{{\cos }^2}{{}}47^\circ }}\) is:

SSC CPO 2020

A)

\(\frac{1}{3}\)

B)

- 3

C)

3

D)

\(-\frac{1}{3}\)

180)

If 4 - 2sin²θ - 5cosθ = 0, 0°< θ < 90°, then the value of cosθ - tanθ is:

SSC CPO 2020

A)

\(\frac{{1 + 2\surd 3}}{2}\)

B)

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

C)

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

D)

\(\frac{{1 - 2\surd 3}}{2}\)