Answer
The right-hand side is equal to $\sin 3x$.
Work Step by Step
By using the identity $\sin \left( \alpha -\beta \right)=\sin \alpha \cos \beta -\cos \alpha \sin \beta $ , the above expression can be simplified as:
$\begin{align}
& \sin \ 5x\ \cos \ 2x-\cos \ 5x\ \sin \ 2x=\sin \left( 5x-2x \right) \\
& =\sin \ 3x
\end{align}$
Thus, the right side of the equation is equal to $\sin 3x$.
Thus, it is proved that left side is equal to the right side.
