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

Prove $1 + {\cot}^{2} x = {\csc}^{2} x$
$1 + {\cot}^{2} x = 1 + {\cos}^{2} \frac{x}{{\sin}^{2} x} = \frac{{\sin}^{2} x + {\cos}^{2} x}{{\sin}^{2} x}$ =
$\frac{1}{{\sin}^{2} x} = {\csc}^{2} x$