[tex]\displaystyle\bf\\2Cos\Big(\frac{x}{2} -\frac{\pi }{6} \Big)=\sqrt{3} \ |:2 \\\\\\Cos\Big(\frac{x}{2} -\frac{\pi }{6} \Big)=\frac{\sqrt{3} }{2} \\\\\\\frac{x}{2} -\frac{\pi }{6} =\pm \ arcCos\frac{\sqrt{3} }{2} +2\pi n,n\in Z\\\\\\\frac{x}{2} -\frac{\pi }{6} =\pm \ \frac{\pi }{6} +2\pi n,n\in Z\\\\\\\frac{x}{2} =\pm \ \frac{\pi }{6} +\frac{\pi }{6} +2\pi n,n\in Z\\\\\\\boxed{x=\pm \ \frac{\pi }{3} +\frac{\pi }{3} +4\pi n,n\in Z}[/tex]

[tex]\displaystyle\bf\\x_{1} =\frac{\pi }{3}+\frac{\pi }{3} +4\pi n,n\in Z \\\\\\x_{1} =\frac{2\pi }{3} +4\pi n,n\in Z \\\\\\x_{2} =-\frac{\pi }{3}+\frac{\pi }{3} +4\pi n,n\in Z \\\\\\x_{2} =4\pi n,n\in Z[/tex]