$-\operatorname{Sin}x+\sqrt{3}\operatorname{Cos}x=1\xrightarrow{\div 2}-\frac{1}{2}\operatorname{Sin}x+\frac{\sqrt{3}}{2}\operatorname{Cos}x=\frac{1}{2}\Rightarrow -\operatorname{Sin}\frac{\pi }{6}\operatorname{Sin}x+\operatorname{Cos}\frac{\pi }{6}\operatorname{Cos}x=\frac{1}{2}\Rightarrow \operatorname{Cos}(x+\frac{\pi }{6})=\frac{1}{2}=\operatorname{Cos}\frac{\pi }{3}\Rightarrow \left\{ _{x+\frac{\pi }{6}=2k\pi -\frac{\pi }{3}}^{x+\frac{\pi }{6}=2k\pi +\frac{\pi }{3}}\Rightarrow \left\{ _{x=2k\pi -\frac{\pi }{2}}^{x=2k\pi +\frac{\pi }{6}} \right. \right.$