Answer
The required value of the $\sin \frac{x}{2}$ is $\pm \sqrt{\frac{1-\cos x}{2}}$ .
Work Step by Step
In order to find the value of $\sin \frac{x}{2}$, the half angle formula is used that is as given below:
${{\sin }^{2}}\alpha =\frac{1-\cos 2\alpha }{2}$
Now, replace $\alpha $ with $\frac{x}{2}$
$\begin{align}
& {{\sin }^{2}}\frac{x}{2}=\frac{1-\cos 2\left( \frac{x}{2} \right)}{2} \\
& =\frac{1-\cos x}{2} \\
& =\pm \sqrt{\frac{1-\cos x}{2}}
\end{align}$
