Answer
$\tan (-x) \cos x=-\sin x$
Work Step by Step
We need to prove the identity $\tan (-x) \cos x=-\sin x$
Since, $\tan x=\dfrac{\sin x}{\cos x}$
Then, we have
$\tan (-x) \cos x=-\tan x \cos x$
$=- \dfrac{\sin x}{\cos x} \times \cos x$
$=-\sin x$
which is the left hand side.
Thus, the identity has been proved.
