4cos^2(x-[latex] \frac{ \pi }{6} [/latex]) - 3 = 0

[latex]4cos^2(x- \frac{ \pi }{6} )-3=0 \\ \\ (2cos(x- \frac{ \pi }{6}) )^2-( \sqrt{3})^2=0 \\ \\ (2cos(x- \frac{ \pi }{6})- \sqrt{3} )(2cos(x- \frac{ \pi }{6})+ \sqrt{3} )=0[/latex] [latex]2cos(x- \frac{ \pi }{6})- \sqrt{3}=0[/latex]  или  [latex]2cos(x- \frac{ \pi }{6})+ \sqrt{3}=0[/latex] [latex]cos(x- \frac{ \pi }{6})= \frac{ \sqrt{3} }{2} [/latex]  или  [latex]cos(x- \frac{ \pi }{6})= -\frac{ \sqrt{3} }{2}[/latex] [latex]x- \frac{ \pi }{6}=бarccos\frac{ \sqrt{3} }{2} +2 \pi n,[/latex] n∈Z  или  [latex]x- \frac{ \pi }{6}=бarccos(-\frac{ \sqrt{3} }{2}) +2 \pi k,[/latex] k∈Z [latex]x- \frac{ \pi }{6} =б \frac{ \pi }{6}+2 \pi n,[/latex] n∈Z  или [latex]x- \frac{ \pi }{6} =б \frac{5 \pi }{6}+2 \pi k,[/latex] k∈Z [latex]x= б\frac{ \pi }{6}+ \frac{ \pi }{6}+2 \pi n,[/latex] n∈Z или [latex]x= б\frac{5 \pi }{6}+ \frac{ \pi }{6}+2 \pi k,[/latex] k∈Z