1)2sinx=корень из(3) 2)tg3x=-1/корень из 3 3)cos(x+пи/3)=-1 4)sin(x-пи/3) +1=0

$1)2sinx=\sqrt{3}$

$sinx=\frac{\sqrt{3}}{2}$

$x=(-1)^{n}\cdot arcsin(\frac{\sqrt{3}}{2})+\pi\cdot n$

$x=(-1)^{n}\cdot\frac{\pi}{3}+\pi\cdot n, n\in Z$

$2)tg3x=-\frac{1}{\sqrt{3}}$

$3x=-\frac{\pi}{6}+\pi\cdot k$

$x=-\frac{\pi}{18}+\frac{\pi}{3}\cdot k,k\in Z$

$3)cos(x+\frac{\pi}{3})=-1$

$x+\frac{\pi}{3}=\pi+2\pi k$

$x=\frac{2\pi}{3}+2\pi k, k\in Z$

$4)sin(x-\frac{\pi}{3})+1=0$

$sin(x-\frac{\pi}{3})=-1$

$x-\frac{\pi}{3}=-\frac{\pi}{2}+2\pi k$

$x=-\frac{\pi}{6}+2\pi k,k\in Z$