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