Answer
The required solution is $\frac{1}{2}\left[ \cos 4x+\cos 10x \right]$.
Work Step by Step
One of the product-to-sum formulas is $\cos \alpha \cos \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)+\cos \left( \alpha +\beta \right) \right]$. So, tn this question, according to the above-mentioned formula, the value of $\alpha $ is $7x$ and the value of $\beta $ is $3x$.
Thus, the expression can be evaluated as provided below.
$\begin{align}
& \cos 7x\cos 3x=\frac{1}{2}\left[ \cos \left( 7x-3x \right)+\cos \left( 7x+3x \right) \right] \\
& =\frac{1}{2}\left[ \cos 4x+\cos 10x \right]
\end{align}$
