#### Answer

$$\tan\theta\cos\theta=\sin\theta$$

#### Work Step by Step

$$A=\tan\theta\cos\theta$$
- Quotient Identity: $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
Therefore, $A$ would be
$$A=\frac{\sin\theta}{\cos\theta}\times\cos\theta$$
$$A=\sin\theta$$
Since no quotients appear here and all functions are of $\theta$ only, we can stop here.