Giải phương trình: \(\sqrt 3 \cos x - \sin x = \sqrt 3 \).

\(\sqrt 3 \cos x - \sin x = \sqrt 3 \)

⇔ \[\frac{{\sqrt 3 }}{2}\cos x - \frac{1}{2}\sin x = \frac{{\sqrt 3 }}{2}\]

⇔ \[\sin \left( {\frac{\pi }{3}} \right)\cos x - \cos \left( {\frac{\pi }{3}} \right)\sin x = \frac{{\sqrt 3 }}{2}\]

⇔ \[\sin \left( {x - \frac{\pi }{3}} \right) = \sin \left( {\frac{\pi }{3}} \right)\]

⇔ \[\left[ \begin{array}{l}x - \frac{\pi }{3} = \frac{\pi }{3} + k2\pi \\x - \frac{\pi }{3} = \pi - \frac{\pi }{3} + k2\pi \end{array} \right.\]

⇔\[\left[ \begin{array}{l}x = 2\frac{\pi }{3} + k2\pi \\x = \pi + k2\pi \end{array} \right.\]