a) $2\sin x-1-0 \Leftrightarrow \sin x=\dfrac{1}{2}=\sin \dfrac{\pi}{6}$

$\Leftrightarrow \left[ \begin{matrix} x=\dfrac{\pi}{6} +k2\pi\\x=\pi – \dfrac{\pi}{6} +k2\pi \end{matrix} \right.  $

$ \Leftrightarrow \left[ \begin{matrix} x=\dfrac{\pi}{6} +k2\pi\\x=\dfrac{5 \pi}{6} +k2\pi \end{matrix} \right.  (k \in \mathbb{Z})$

b) $2\cos (x-15^o)+1=0 \Leftrightarrow \cos (x-15^o)=-\dfrac{1}{2}=\cos 120^o$

$\Leftrightarrow \left[ \begin{matrix} x-15^o=120^o+k360^o\\x-15^o=-120^o+k360^o \end{matrix} \right.$

$\Leftrightarrow \left[\begin{matrix} x=135^o+k360^o\\ x=-105^o+k360^o \end{matrix} \right. (k \in \mathbb{Z})$

c) $\sqrt{3} \tan x=3 \Leftrightarrow \tan x=\sqrt{3}=\tan \dfrac{\pi}{3} $

$\Leftrightarrow x= \dfrac{\pi}{3}+k\pi, k \in \mathbb{Z}.$

d) $3\cot (2x+1)=-1 \Leftrightarrow \cot (2x+1)=\dfrac{-1}{3} \Leftrightarrow 2x+1=arccot \left(-\dfrac{1}{3}\right)+k\pi   $

$\Leftrightarrow x=-\dfrac{1}{2}+\dfrac{1}{2} arccot \left(-\dfrac{1}{3} \right)+\dfrac{k\pi}{2}, k \in \mathbb{Z}$

a) $x=\dfrac{\pi}{5}+k2\pi; x=\dfrac{k2\pi}{3}, k \in \mathbb{Z}$

b) $x=\dfrac{\pi}{4}-1+k\dfrac{\pi}{2}, k \in \mathbb{Z}$

c) $ x=\dfrac{\pi}{6}+k2\pi; x=\dfrac{5\pi}{18}+\dfrac{k2\pi}{3}, k \in \mathbb{Z}$

d) $x=-\dfrac{\pi}{6}+\dfrac{k2\pi}{3}; x=-\dfrac{\pi}{10}+\dfrac{k2\pi}{5}, k \in \mathbb{Z}$

a) $x=\dfrac{\pi}{6}+k2\pi, k \in \mathbb{Z}$

b) $x=\dfrac{\pi}{6}+k2\pi; x= \dfrac{5\pi}{6}+k2\pi , k \in \mathbb{Z}$.

a) Tập nghiệm của phương trình $S=\left\{ \dfrac{\pi}{12}; \dfrac{13\pi}{12}; \dfrac{5 \pi}{12}; \dfrac{17\pi}{12} \right\}$

b) Tập nghiệm của phương trình  $S=\left\{-75^o; 105^o; 285^o \right\}$