$\sin^2x - \cos^22x = 0$
$\Leftrightarrow\dfrac{1 - \cos2x}{2} - \cos^22x = 0$
$\Leftrightarrow 2\cos^22x + \cos2x - 1 = 0$
$\Leftrightarrow\left[\begin{array}{l}\cos2x = -1\\\cos2x =\dfrac{1}{2}\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}2x = \pi + k2\pi\\2x =\pm \dfrac{\pi}{3} + k2\pi\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{2} + k\pi\\x =\pm \dfrac{\pi}{6} + k\pi\end{array}\right.\qquad (k\in \Bbb Z)$
