## Precalculus (6th Edition) Blitzer

$\tan (-x) \cos x=-\sin x$
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.