Giải phương trình:

\(2\cos \frac{x}{2} + \sqrt 3 = 0\);

\(2\cos \frac{x}{2} + \sqrt 3 = 0\)

\( \Leftrightarrow \cos \frac{x}{2} = - \frac{{\sqrt 3 }}{2}\)

\( \Leftrightarrow \cos \frac{x}{2} = \cos \frac{{5\pi }}{6}\)      (do \(\cos \frac{{5\pi }}{6} = - \frac{{\sqrt 3 }}{2}\))

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

\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{{5\pi }}{3} + k4\pi \\x = - \frac{{5\pi }}{3} + k4\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\).