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