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