Answer
The required solution is $2\sin \frac{3x}{2}\cos \frac{x}{2}$.
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 $x$ and the value of $\beta $ is $2x$.
Now, the expression can be evaluated as provided below:
$\begin{align}
& \sin x+\sin 2x=2\sin \frac{x+2x}{2}\cos \frac{x-2x}{2} \\
& =2\sin \frac{3x}{2}\cos \frac{-x}{2}
\end{align}$
Thus, applying the even-odd identity, which is $\cos (-x)=\cos x$, the expression can be further evaluated as given below:
$2\sin \frac{3x}{2}\cos \frac{-x}{2}=2\sin \frac{3x}{2}\cos \frac{x}{2}$
Hence, the provided expression can be written as $2\sin \frac{3x}{2}\cos \frac{x}{2}$. So, it is not possible to find the exact value.
