Verified answer

[tex]\displaystyl\bf\\Cosx=-\dfrac{\sqrt{3} }{2}\\\\\\x=\pm \ arcCos\Big(-\dfrac{\sqrt{3} }{2}\Big)+2\pi n,n\in Z\\\\\\x=\pm \ \dfrac{5\pi }{6} +2\pi n,n\in Z[/tex]