Answer
The right side is equal to $\cos \frac{x}{2}$.
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:
$\begin{align}
& \cos \frac{5x}{2}\cos 2x+\sin \frac{5x}{2}\sin 2x=\cos \left( \frac{5x}{2}-2x \right) \\
& =\cos \left( \frac{5x-4x}{2} \right) \\
& =\cos \frac{x}{2}
\end{align}$
Thus, the right side of the equation is equal to $\cos \frac{x}{2}$.
Thus, it is proved that left side is equal to the right side.
