Question

2sin(2x-п/3)=корень из 3

Answer 1

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