Question

2sin(2x-п/3)= минус $\sqrt{3}$

Answer 1

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