SSC CGL 2021 PYQ — Question 61

The correct answer is Option 1 i.e sec²θ.

$\sqrt{sec^2 \theta + cosec^2 \theta} \times \frac{Sin \theta (1 + Cos \theta)}{1 + Cos \theta - Sin^2 \theta}$ can be written as,

⇒$\sqrt{\frac{1}{Cos^2 \theta} + \frac{1}{Sin^2 \theta}} \times \frac{ Sin​​ \theta (1 + Cos \theta)}{(1 + Cos \theta)(Cos \theta}$

⇒ $\sqrt{sec^2 \theta \times cosec^2 \theta} \times \frac{Sin \theta }{Cos \theta}$

⇒ Sec$\theta$ × Cosec$\theta$ × $\frac{Sin \theta }{Cos \theta}$

⇒  Sec$\theta$ × Cosec$\theta$ × $\frac{Sec \theta}{Cosec \theta}$

⇒ $Sec^2 \theta$.