Answer
$$\sin^2\theta(\csc^2\theta-1)=\cos^2\theta$$
Work Step by Step
$$A=\sin^2\theta(\csc^2\theta-1)$$
- Pythagorean Identity:
$$\cot^2\theta+1=\csc^2\theta$$
Replace into $A$:
$$A=\sin^2\theta(\cot^2\theta+1-1)$$
$$A=\sin^2\theta(\cot^2\theta)$$
- Quotient Identity:
$$\cot\theta=\frac{\cos\theta}{\sin\theta}$$
Replace into $A$:
$$A=\sin^2\theta\times\frac{\cos^2\theta}{\sin^2\theta}$$
$$A=\cos^2\theta$$
