Question

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

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

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

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

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

Замена: $cos x = t, t in [-1; 1]$

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

$t_{1}=-1$

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

Обратная замена:

$cos x = -1$

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

Ответ: $x = pi + 2pi n, n in Z$