Question

sin^2 x + 2 cos x + 2 = 0
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Answer 1

$\sin^{2}x + 2\cos x + 2 = 0$

$1 - \cos^{2}x + 2 \cos x + 2 = 0$

$-\cos^{2}x + 2\cos x + 3 = 0$

$\cos^{2}x - 2\cos x - 3 = 0$

Замена: $\cos x = t, \ t \in [-1; \ 1]$

$t^{2} - 2t - 3 = 0$

$t_{1}=-1$

$t_{2} = 3 \notin [-1; \ 1]$

Обратная замена:

$\cos x = -1$

$x = \pi + 2\pi n, \ n \in Z$

Ответ: $x = \pi + 2\pi n, \ n \in Z$