SSC CGL 2021 PYQ — Question 54

The correct answer is option 2 i.e. cosec³ θ

== $\sqrt{\frac{\frac{1}{cos^2 \theta} +\frac{1}{sin^2 \theta}}{\frac{sin^2 \theta}{cos^2 \theta} - sin^2 \theta}}$

= $\sqrt{\frac{\frac{1}{sin^2 \theta \times cos^2 \theta}}{\frac{sin^2 \theta(1 - sin ^2 \theta)}{cos^2 \theta}}}$

= $\sqrt{\frac{1}{sin^6 \theta}}$

= cosec³$\theta$.