$a)$ 2sin(x+15độ)=3
$sin(x+15^o)=\dfrac{3}{2}$
Vì $\dfrac{3}{2}>1$ mà $-1≤sinx≤1$
$⇒$ Phương trình vô nghiệm
$b)$sin(4x+1/2)=1/3
$⇔$\(\left[ \begin{array}{l}4x+\dfrac{1}{2}=arcsin(\dfrac{1}{3})+k2\pi\\4x+\dfrac{1}{2}=\pi-arcsin(\dfrac{1}{3})+k\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}4x=-\dfrac{1}{2}+arcsin(\dfrac{1}{3})+k2\pi\\4x=-\dfrac{1}{2}+\pi-arcsin(\dfrac{1}{3})+k2\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=-\dfrac{1}{8}+\dfrac{1}{4}arcsin(\dfrac{1}{3})+\dfrac{k\pi}{2}\\x=-\dfrac{1}{8}+\dfrac{1}{4}\pi-\dfrac{1}{4}arcsin(\dfrac{1}{3})+\dfrac{k\pi}{2}\end{array} \right.\)
