Answer
The expression on the left-side is equal to the expression on the right-side.
Work Step by Step
The given expression on the left side $\tan \frac{x}{2}\left( 1+\cos x \right)$ can be simplified by using the half-angle formula. As per the half-angle formula, $\tan \frac{x}{2}=\frac{\sin x}{1+\cos x}$.
$\begin{align}
& \tan \frac{x}{2}\left( 1+\cos x \right)=\frac{\sin x}{1+\cos x}.\left( 1+\cos x \right) \\
& =\sin x
\end{align}$
Hence, the expression on the left-side is equal to the expression on the right-side.
