Question

Prove the following identity:
$\left(xi\right)\frac{(1+\sin A)}{(1-\sin A)}=\frac{(\text{cosec}A+1)}{(\text{cosec}A-1)}$

Answer 1

First we consider Right Hand Side (RHS),
$\frac{(\text{cosec}A+1)}{(\text{cosec}A-1)}$

We know that, $\text{cosec}A=\frac{1}{\sin A}$, so
$=\frac{(\frac{1}{\sin A}+1)}{(\frac{1}{\sin A}-1)}$

$=\frac{(1+\sin A)}{(1-\sin A)}$

Therefore, LHS = RHS
Hence Proved.