# How do you prove csc^2(x)-cot^2(x)=1?

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