Answer
See below.
Work Step by Step
$LHS=(1+cos\theta)tan(\frac{\theta}{2})=(1+cos\theta)(\frac{sin\theta}{1+cos\theta})=sin\theta=RHS$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.