# How do you verify -(1/2)sec²(x) = -2sin²(x)csc²(2x)?

$\sin 2 A = 2 \sin A \cos A$
$- 2 {\sin}^{2} x {\csc}^{2} 2 x = - \frac{2 {\sin}^{2} x}{{\sin}^{2} 2 x} = - \frac{2 {\sin}^{2} x}{4 {\sin}^{2} x {\cos}^{2} x} = - \frac{1}{2} {\sec}^{2} x$