Answer
$2\cos\frac{11x}{2}\cos\frac{7x}{2}$
Work Step by Step
Use the third Sum-to-Product Formula, $\cos x+\cos y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}$.
$\cos 9x+\cos 2x$
$=2\cos\frac{9x+2x}{2}\cos\frac{9x-2x}{2}$
$=2\cos\frac{11x}{2}\cos\frac{7x}{2}$