Answer
See the steps.
Work Step by Step
$RHS =\dfrac{\tan{\theta} +\sin{\theta}}{2\tan{\theta}}$
Dividing both numerator and denominator by $\tan{\theta}$
$RHS = \dfrac{1+\dfrac{\sin{\theta}}{\tan{\theta}}}{{2}} = \dfrac{1+\cos{\theta}}{2}= \cos^2{\dfrac{\theta}{2}} = LHS$