a,
$\sin\left(\cos(x+\dfrac{\pi}{4}\right)=0$
$\to \cos\left(x+\dfrac{\pi}{4}\right)=k\pi$
$-1\le k\pi\le 1\to k=0$
$\cos\left(x+\dfrac{\pi}{4}\right)=0$
$\to x+\dfrac{\pi}{4}=\dfrac{\pi}{2}+k\pi$
$\to x=\dfrac{\pi}{4}+k\pi$
b,
$\sin^23x=\dfrac{1}{4}$
$\to \dfrac{1-\cos6x}{2}=\dfrac{1}{4}$
$\to \cos6x=\dfrac{1}{2}$
$\to x=\pm\dfrac{\pi}{18}+\dfrac{k\pi}{3}$
c,
$\sin2x-\sin x=0$
$\to \sin2x=\sin x$
$\to \left[ \begin{array}{l}2x=x+k2\pi \\2x=\pi-x+k2\pi \end{array} \right.$
$\to \left[ \begin{array}{l}x=k2\pi \\x=\dfrac{\pi}{3}+\dfrac{k2\pi}{3}\end{array} \right.$
