Question

Решить уравнение 2sin2x - корень из 3 sinx =0

Answer 1

$2Sin2x-\sqrt{3}Sinx=0\\\\2*2SinxCosx-\sqrt{3}Sinx=0\\\\4SinxCosx-\sqrt{3}Sinx=0\\\\Sinx(4Cosx-\sqrt{3})=0\\\\1)Sinx=0\\\\x=\pi n,n\in Z\\\\2)4Cosx-\sqrt{3}=0\\\\4Cosx=\sqrt{3}\\\\Cosx=\frac{\sqrt{3} }{4}\\\\x=\pm arcCos\frac{\sqrt{3}}{4}+2\pi n,n\in Z$