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