Question

Помогите,пожалуйста,с тригонометрией!!!!!!Уравнения

Answer 1

$1) \; sin2x-\sqrt3cosx=0\\2sinxcosx-\sqrt3cosx=0\\cosx(2sinx-\sqrt3)=0\\\\cosx=0\\x=\frac{\pi}{2}+\pi n, \; n\in Z;\\\\2sinx-\sqrt3=0\\sinx=\frac{\sqrt3}{2}\\x=(-1)^k\frac{\pi}{3}+\pi k, \; k\in Z;\\\\\\ 2) \; sin2x-\sqrt3sinx=0\\2sinxcosx-\sqrt3sinx=0\\sinx(2cosx-\sqrt3)=0\\\\sinx=0\\x=\pi n, \; n\in Z;\\\\2cosx-\sqrt3 =0\\cosx=\frac{\sqrt3}{2}\\x=\pm \frac{\pi}{6}+2\pi k, \; k\in Z;$


$3) \; 2cos2x+1=2cos^2x\\2cos2x+1=cos2x+1\\cos2x=0\\2x=\frac{\pi}{2}+\pi n\\x=\frac{\pi}{4}+\frac{\pi}{2};\\\\\\4) \; sin2x+2sinx=0\\2sinxcosx+2sinx=0\\2sinx(cosx+1)=0\\\\sinx=0\\x=\pi n, \; n\in Z;\\\\cosx+1=0\\cosx=-1\\x=\pi +2\pi k, \; k\in Z$