Question

√2 * cos (x)+ sin (2 * x) = 0

Answer 1

$\sqrt{2}\cos x + \sin2x = 0\\\sqrt{2}\cos x + 2\sin x\cos x = 0\\\cos x(\sqrt{2} + 2\sin x) = 0\\\cos x = 0~u~\sqrt{2} + 2\sin x = 0$

$\cos x = 0\\x = \frac{\pi}{2} + \pi k, k\in Z$

$\sqrt{2} + 2\sin x = 0\\\sin x = -\frac{\sqrt{2}}{2}\\x = -\frac{\pi}{4} + 2\pi k, k\in Z\\x = -\frac{3\pi}{4} + 2\pi k, k\in Z$

Ответ: $\frac{\pi}{2} + \pi k; \frac{\pi}{4} + 2\pi k; \frac{3\pi}{4} + 2\pi k, k\in Z$.