Answer
$x=n\pi$
$x=\frac{\pi}{2}+n\pi$
where $n$ is an integer.
Work Step by Step
$sin~4x=sin~2(2x)=2~sin~2x~cos~2x$
$sin~4x=-2~sin~2x$
$2~sin~2x~cos~2x+2~sin~2x=0$
$2~sin~2x(cos~2x+1)=0$
$sin~2x=0$ or $cos~2x=-1$
$sin~2x=0$
$2x=0$
$x=0$ and
$2x=\pi$
$x=\frac{\pi}{2}$
$cos~2x=-1$
$2x=\pi$
$x=\frac{\pi}{2}$
The period of both $sin~2x$ and $cos~2x$ is $\pi$. The general solutions are:
$x=0+n\pi=n\pi$
$x=\frac{\pi}{2}+n\pi$
where $n$ is an integer.
