Giải phương trình: \(\sqrt 3 \sin x + \cos x = 1\).

\(\begin{array}{l}\sqrt 3 \sin x + \cos x = 1\\ \Leftrightarrow \frac{{\sqrt 3 }}{2}\sin x + \frac{1}{2}\cos x = \frac{1}{2}\\ \Leftrightarrow \sin x.\cos \frac{\pi }{6} + \cos x.\sin \frac{\pi }{6} = \frac{1}{2}\\ \Leftrightarrow \sin \left( {x + \frac{\pi }{6}} \right) = \frac{1}{2}\\ \Leftrightarrow \left[ \begin{array}{l}x + \frac{\pi }{6} = \frac{\pi }{6} + k2\pi \\x + \frac{\pi }{6} = \frac{{5\pi }}{6} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\\ \Leftrightarrow \left[ \begin{array}{l}x = k2\pi \\x = \frac{{2\pi }}{3} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\end{array}\).