[ Exponential functions and logarithms (other).]

For what values of $a$ and $b$ is the equality

$$
\sin a + \sin b = \sin (a + b)
$$

possible?
Bring the equality to the form

$$
\sin \frac{a}{2} \sin \frac{b}{2} \sin \frac{a+b}{2}=0
$$

## Answer

Either $a=2 k \pi$, or $b=2 l \pi$, or $a+b=2 m \pi$.