Answer
See the explanation below.
Work Step by Step
Let us consider the right side of the given expression:
$\frac{\sin x}{1-\cos x}$
By using the trigonometric identity $\tan \frac{x}{2}=\frac{1-\cos x}{\sin x}$, the above expression can be further simplified by multiplying the numerator and denominator by $\frac{1}{\sin x}$
$\begin{align}
& \frac{\sin x}{1-\cos x}=\frac{\left( \sin x \right)\times \frac{1}{\sin x}}{\left( 1-\cos x \right)\times \frac{1}{\sin x}} \\
& =\frac{\frac{\sin x}{\sin x}}{\frac{1-\cos x}{\sin x}} \\
& =\frac{1}{\tan \frac{x}{2}} \\
& =\cot \frac{x}{2}
\end{align}$
Hence, the left side of the given expression is equal to the right side, which is $\cot \frac{x}{2}=\frac{\sin x}{1-\cos x}$.
