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