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