# How do you prove 1+cos2x=2/(1+tan^2x) using the double angle identity?

$\cos 2 x = 2 {\cos}^{2} x - 1$
${\tan}^{2} x + 1 = {\sec}^{2} x$
$1 + \cos 2 x = 2 {\cos}^{2} x = \frac{2}{\sec} ^ 2 x = \frac{2}{1 + {\tan}^{2} x}$