Answer
See explanations.
Work Step by Step
Step 1. $LHS=\frac{\frac{1}{sin\theta}-sin\theta}{sin\theta}=\frac{1-sin^2\theta}{sin^2\theta}=\frac{cos^2\theta}{sin^2\theta}$
Step 2. $RHS=cot^2\theta=\frac{cos^2\theta}{sin^2\theta}$
Step 3. Since $LHS=RHS$, we verified the identify.
