$\begin{array}{l} \cos 4x = \dfrac{{\sqrt 3 }}{2}\\ \Leftrightarrow \cos 4x = \cos \dfrac{\pi }{6}\\ \Leftrightarrow \left[ \begin{array}{l} 4x = \dfrac{\pi }{6} + k2\pi \\ 4x = - \dfrac{\pi }{6} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = \dfrac{\pi }{{24}} + \dfrac{{k\pi }}{2}\\ x = - \dfrac{\pi }{{24}} + \dfrac{{k\pi }}{2} \end{array} \right.\left( {k \in \mathbb{Z}} \right) \end{array}$
