Answer
The required solution is $-2\sin 8x\sin x$.
Work Step by Step
One of the sum-to-product formula is $\cos \alpha -\cos \beta =-2\sin \frac{\alpha +\beta }{2}\sin \frac{\alpha -\beta }{2}$. So, in this question, according to the above-mentioned formula, the value of $\alpha $ is $9x$ and the value of $\beta $ is $7x$.
Thus, the expression can be evaluated as provided below:
$\begin{align}
& \cos 9x-\cos 7x=-2\sin \frac{9x+7x}{2}\sin \frac{9x-7x}{2} \\
& =-2\sin \frac{16x}{2}\sin \frac{2x}{2} \\
& =-2\sin 8x\sin x
\end{align}$
Hence, the given expression can be written as $-2\sin 8x\sin x$. So, it is not possible to find the exact value.
