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