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