Answer
The required value of the sin 2x is 2 sin x cos x.
Work Step by Step
In order to find the value of sin 2x, the double angle formula is used that is as shown below:
$Sin\left( \alpha +\beta \right)=\sin \alpha \,\cos \beta +\cos \alpha +\,\sin \beta $
Now, consider $\alpha $ and $\beta $ as x in sin (x+x); then the formula becomes:
$\begin{align}
& Sin\left( x+x \right)=\sin x\,\cos x+\cos x\,\sin x \\
& sin\,2x=2\,\sin x\,\cos x
\end{align}$
Hence, the required value of the sin 2x is 2 sin x cos x.
