SSC CGL 2024 PYQ — Question 56

The correct answer is option 1 i.e.  ${ \sqrt{3} }$

let's, ${{1} \over 1 - sinθ} + {{1} \over 1 + sinθ} = 4secθ, (0 < θ < 90 )$

⇒ ${{(1 + sin \theta) + (1 - sin\theta)} \over {(1 - sin\theta)(1 + sin\theta)}} = {4 sec\theta}$

⇒ ${2\over {(1 - sin^2\theta)}} = {4 \over cos\theta}$

⇒ 4 cos²θ = 2cosθ

⇒ cosθ = 1/2

⇒ θ = 60°

then, (cot60° + cosec60°) 

 ⇒ ${ 1\over \sqrt{3}} + {2 \over \sqrt{3}}$

⇒ $3 \over \sqrt{3}$ = ${ \sqrt{3} }$

​So the expected answer is ${ \sqrt{3} }$.