SSC CGL 2024 PYQ — Question 69

The correct answer is option 3 i.e. cotθ.

cosec²A - cot²A = 1

According to the given question,

$\frac{1}{cosecθ - cotθ} - \frac{1}{sinθ}$

⇒ $(\frac{1}{cosecθ - cotθ} \times \frac{cosec \theta + \cot\theta}{cosec \theta + cot\theta}) - \frac{1}{sinθ}$

⇒ $(\frac{cosec \theta + \cot\theta}{cosec^2 \theta + cot^2\theta}) - \frac{1}{sinθ}$

⇒ cosecθ + cotθ - cosecθ

⇒ cotθ