$cos(2x) + sin^2 x = 0 $
$ 1-2sin^2 x + sin^2 x= 0$
$ 1 - sin^2 x = 0 $
$ sin^2 x = 1$
$ sin x = \pm 1 \; ⇒ \; x = \frac{\pi}{2} + k\pi; \qquad k \in \mathbb{Z} $
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