$\begin{array}{l}
2{\cos ^2}x = 1\\
\Leftrightarrow {\cos ^2}x = \frac{1}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = - \frac{1}{{\sqrt 2 }}\\
\cos x = \frac{1}{{\sqrt 2 }}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \pm \frac{{3\pi }}{4} + k2\pi \\
x = \pm \frac{\pi }{4} + k2\pi
\end{array} \right.\,\,\,\left( {k \in Z} \right).
\end{array}$
