How do you prove (1+cos^2x)/sin^2x=2csc^2x-1?

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