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