Answer
The required solution is $2\sin 5x\cos 3x$.
Work Step by Step
One of the sum-to-product formula is $\sin \alpha +\sin \beta =2\sin \frac{\alpha +\beta }{2}\cos \frac{\alpha -\beta }{2}$. So, in this question, according to the above-mentioned formula, the value of $\alpha $ is $8x$ and the value of $\beta $ is $2x$.
Thus, the expression can be evaluated as provided below:
$\begin{align}
& \sin 8x+\sin 2x=2\sin \frac{8x+2x}{2}\cos \frac{8x-2x}{2} \\
& =2\sin \frac{10x}{2}\cos \frac{6x}{2} \\
& =2\sin 5x\cos 3x
\end{align}$
Hence, the provided expression can be written as $2\sin 5x\cos 3x$. It is not possible to find the exact value.
