#### Answer

$\cos 2\theta=\frac{2-\sec^2 \theta}{\sec^2 \theta}$

#### Work Step by Step

Start with the right side:
$\frac{2-\sec^2 \theta}{\sec^2 \theta}$
Break it into two fractions and simplify:
$=\frac{2}{\sec^2 \theta}-\frac{\sec^2 \theta}{\sec^2 \theta}$
$=\frac{2}{\frac{1}{\cos^2\theta}}-1$
$=2\cos^2\theta-1$
$=\cos 2\theta$
Since this equals the left side, the identity has been proven.