SSC CGL 2020 PYQ — Question 98

The correct answer is option 2 i.e. 2-√3

Here it is given that,

cos(2θ + 54º) = sinθ

Sin(90 - 2θ - 54º) = sinθ

-2θ + 36 = θ

3θ = 36

θ = 12°

Tan5θ = Tan60 = √3

Cosec 5θ/2 = Cosec30° = 2

Now, $\frac{1}{tan 5\theta + cosec \frac{5 \theta}{2}} = \frac{1}{\sqrt3 + 2}$

On rationalizing further we get,

= (2 - √3)/(4 - 3)

= (2 - √3).