a) $\sin x= \frac{ 1}{2}= \sin \frac{ \pi}{6} \Rightarrow \left[ \begin{array}{l} x= \frac{ \pi}{6}+k2\pi \\ x= \pi- \frac{ \pi}{6}+k2\pi \end{array} \right. $ hay $x= \frac{ 5\pi}{6}+k2\pi$
b) $\cos \frac{ x}{3}= \frac{ \sqrt{ 2}}{2}= \cos \frac{ \pi}{4} \Rightarrow \frac{ x}{3}= \pm \frac{ \pi}{4}+k2\pi \Leftrightarrow x= \pm \frac{ 3\pi}{4}+k6\pi$
c) $\tan \frac{ x}{4}= \sqrt{ 3}\Rightarrow \tan \frac{ x}{4}= \tan \frac{ \pi}{3} \Rightarrow \frac{ x}{4}= \frac{ \pi}{3}+k\pi$
Vậy $x= \frac{ 4\pi}{3}+4k\pi$
d) $\cot 3x= - \frac{ \sqrt{ 3}}{3}=\cot \left( -\frac{ \pi}{3} \right) \Rightarrow 3x= -\frac{ \pi}{3}+k\pi$
$x=-\frac{ \pi}{9}+k \frac{ \pi}{3}$
$(k\in Z)$