Question

Решите уравнение: sin²x + 2cosx+2=0

Answer 1

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

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

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

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

Замена: $cos x = t, t in [-1; 1]$

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

$left[begin{array}{ccc}t_{1} = -1 \t_{2} =3 > 1\end{array}right$

Обратная замена:

$cos x = -1$

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

Ответ: $x = pi + 2pi n, n in Z$