Answer
See the steps.
Work Step by Step
$RHS =\dfrac{1-\tan^2 {\theta}}{1+\tan^2 {\theta}} =\dfrac{1-\tan^2 {\theta}}{\sec^2{\theta}}$
$RHS = \dfrac{1}{\sec^2{\theta}} - \dfrac{\tan^2{\theta}}{\sec^2{\theta}}$
$RHS = \cos^2{\theta} - \sin^2{\theta} = \cos{2\theta} = LHS$
