# How do you prove 1 + cot2 x = csc2 x?

We have to prove 1 + cot2x = csc2x

### Solution

1 + cot2x

Expressing the given expression in terms of sin and cos

$\frac{sin^{2}x}{\sin ^{2}x} + \frac{cos^{2}x}{\sin ^{2}x}$

=$\frac{cos^{2}x + sin^{2}x}{\sin ^{2}x}$

= $\frac{1}{\sin ^{2}x}= csc^{2}x$

= RHS

Hence Proved