Question

2sin(2x-п/3)=корень из 3

Answer 1

$2sin(2x- frac{pi}{3} )= sqrt{3} \ \ sin(2x-frac{pi}{3} )= frac{sqrt{3}}{2} \ \ 2x-frac{pi}{3} =(-1)^kcdot arcsin( frac{sqrt{3}}{2})+ pi k,k in Z\ \ 2x-frac{pi}{3} =(-1)^kcdotfrac{pi}{3} + pi k,k in Z,,, |+frac{pi}{3} \ \ 2x=(-1)^kcdotfrac{pi}{3} +frac{pi}{3} + pi k,k in Z,,,, |:2\ \ \ boxed{x=(-1)^kcdotfrac{pi}{6}+frac{pi}{6} +frac{pi k}{2} ,k in Z }$