Answer
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.
Work Step by Step
$sin~x=\sqrt 3-sin~x$
$2~sin~x=\sqrt 3$
$sin~x=\frac{\sqrt 3}{2}$
The period of $sin~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$x=\frac{\pi}{3}$ and $x=\frac{2\pi}{3}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{\pi}{3}+2n\pi$ and $x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.
