Answer
The required solution is $\frac{1}{2}\left[ \cos 7x+\cos 11x \right]$.
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, in this question, according to the above-mentioned formula, the value of $\alpha $ is $9x$ and the value of $\beta $ is $2x$.
Thus, the expression can be evaluated as provided below:
$\begin{align}
& \cos 9x\cos 2x=\frac{1}{2}\left[ \cos \left( 9x-2x \right)+\cos \left( 9x+2x \right) \right] \\
& =\frac{1}{2}\left[ \cos 7x+\cos 11x \right]
\end{align}$
