2sinx-корень3tgx-2корень3cosx+3=0

[latex]2sin x- sqrt{3} tg x-2sqrt{3}cos x+3=0|cdot (cos xe 0)\ \ 2sin xcos x-sqrt{3}sin x-2sqrt{3}cos^2 x+3cos x=0\ \ sin x(2cos x-sqrt{3})-sqrt{3}cos x(2cos x-sqrt{3})=0\ \ (2cos x-sqrt{3})(sin -sqrt{3}cos x)=0\ \ 2cos x-sqrt{3}=0\ \ cos x= frac{sqrt{3}}{2} \ \ oxed{x_1=pm frac{pi}{6}+ 2pi n,n in Z}\ \ \ sin x-sqrt{3}cos x=0|:cos x\ \ tg x=sqrt{3}\ \ oxed{x_2= frac{pi}{3}+ pi n,n in Z }[/latex]