Answer
See below.
Work Step by Step
$LHS=\frac{1-cos\theta}{1+cos\theta}=\frac{1-cos\theta}{1+cos\theta}\times\frac{1-cos\theta}{1-cos\theta}=\frac{(1-cos\theta)^2}{1-cos^2\theta}=\frac{(1-cos\theta)^2}{sin^2\theta}=(\frac{1-cos\theta}{sin\theta})^2=(csc\theta-cot\theta)^2=RHS$
