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