Prove that ? Sec^2 x + cosec^2 x = sec^2 x . cosec^2 x

$L H S = {\sec}^{2} x + {\csc}^{2} x$
$= \frac{1}{{\cos}^{2} x} + \frac{1}{{\sin}^{2} x}$
$= \frac{{\sin}^{2} x + {\cos}^{2} x}{{\sin}^{2} x \cdot {\cos}^{2} x}$
$= \frac{1}{{\cos}^{2} x \cdot {\csc}^{2} x} = {\sec}^{2} x \cdot {\csc}^{2} x = R H S$