SSC CGL 2024 PYQ — Question 55

The correct answer is option 2 i.e. 2 cosecθ.

$\sqrt{secθ+1\over secθ-1}\ +\ \sqrt{secθ-1\over secθ+1}$

$=\frac{\sqrt{sec\theta+1}}{\sqrt{sec\theta-1}}+\frac{\sqrt{sec\theta-1}}{\sqrt{sec\theta+1}}$

$=\frac{(sec\theta+1)+(sec\theta-1)}{\sqrt{sec^2\theta-1}}$

$=\frac{2sec\theta}{tan\theta}$   $[ ∵ tan\theta=\sqrt{sec^2\theta-1}]$

= 2 × (1/cosθ) × (cosθ/sinθ)   [∵ secθ = 1/cosθ and tanθ = sinθ/cosθ]

= 2/sinθ   [∵ sinθ = 1/cosecθ]

= 2cosecθ