# How do you verify trigonometric Identities: cot^2 x +csc^2 x = 2csc^2 x - 1?

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