251)

If tan3θ⋅tan7θ = 1, where 7θ is an acute angle, then find the value of cot15θ.

SSC CGL 2022

A)

\(-\sqrt3\)

B)

-1

C)

1

D)

\(\sqrt3\)

252)

Find the value of s\(ecθ - tanθ, if secθ + tanθ = \sqrt5\) .

SSC CGL 2022

A)

\(5\frac{\sqrt5}{5}\)

B)

\(5\frac{1}{5}\)

C)

5

D)

\(\sqrt5\)

253)

If \(2 sinθ + 2 sin^2θ=2\), then the value of \(2 cos^4θ + 2 cos^2θ\) is:

 

SSC CGL 2022

A)

1

B)

2

C)

4

D)

0

254)

If \(sec A = {5\over4}\) , then the value of \(\rm \frac{\tan A}{1 + \tan^2A} - \frac{\sin A}{\sec A}\)is:

SSC CGL 2022

A)

0

B)

1

C)

2

D)

3

255)

If \(cos θ + cos^2θ =1\), find the value of \(​​​​​​​\sqrt{\sin^4θ + \cos^2θ}\)

SSC CGL 2022

A)

\(\sqrt{2}cos θ \)

B)

\(\sqrt{2} sin θ\)

C)

2cos θ 

D)

2sin θ

256)

If sin A = 4/5, then what is the value of sin2 A?

SSC CGL 2022

A)

48/25

B)

36/25

C)

26/25

D)

16/25

257)

If \(sec\theta = x + {1\over 4x}\) (0° < θ < 90°), then secθ + tanθ is equal to 

A)

x/2

B)

2x

C)

x

D)

1/2x

258)

If \(tan\theta = {a \over b}\), then \({a.sin\theta + b.cos\theta \over {a.sin\theta - b.cos\theta}}\) is:

A)

\(a \over a^2 + b^2\)

B)

\(b \over a^2 + b^2\)

C)

\(a^2 - b^2 \over a^2 + b^2\)

D)

\(a^2+b^2 \over a^2 - b^2\)

259)

If \(sec \theta= {113 \over 112}\) and θ lies in the 4th Quadrant, then the value of sinθ is 

A)

15/113

B)

-15/113

C)

112/113

D)

-112/113

260)

If \(cot\theta = {9 \over 40} \) and \(\pi < θ < {3\pi \over 2} \), then the value of cosecθ is 

A)

41/40

B)

-41/40

C)

9/40

D)

40/9