#### Answer

$$-\tan x\cos x=\sin(-x)$$
$\text{C}$ is the answer.

#### Work Step by Step

$$A=-\tan x\cos x$$
A Quotient Identity related to $\tan x$ states that $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
That means we can rewrite $A$ as follows:
$$A=-\frac{\sin x}{\cos x}\cos x$$
$$A=-\sin x$$
Also, from Negative-Angle Identities, we know
$$\sin(-\theta)=-\sin\theta$$
Therefore, $$A=\sin(-x)$$
$\text{C}$ is the answer.