$cos^22x=\dfrac{1}{2}$
$⇔ cos2x=±\dfrac{\sqrt[]{2}}{2}$
+) $cos2x=\dfrac{\sqrt[]{2}}{2}$
$⇔ cos2x=cos\dfrac{\pi}{4}$
$⇔ \left[ \begin{array}{l}2x=\dfrac{\pi}{4}+k2\pi\\x=-\dfrac{\pi}{4}+k2\pi\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=\dfrac{\pi}{8}+k\pi\\x=-\dfrac{\pi}{8}+k\pi\end{array} \right.$ $(k∈Z)$
+) $cos2x=-\dfrac{\sqrt[]{2}}{2}$
$⇔ cos2x=cos\dfrac{3\pi}{4}$
$⇔ \left[ \begin{array}{l}2x=\dfrac{3\pi}{4}+m2\pi\\2x=-\dfrac{3\pi}{4}+m2\pi\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=\dfrac{3\pi}{8}+m\pi\\x=-\dfrac{3\pi}{8}+m\pi\end{array} \right.$ $(m∈Z)$
