Question

Решить тригонометрическое уравнение

Answer 1

$\sqrt{2} \sin ^{2} ( \frac{\pi}{2} + x) = - \cos(x) \\ \sqrt{2} \cos ^{2} (x) + \cos(x) = 0 \\ \cos(x) ( \sqrt{2} \cos(x) + 1) = 0 \\ \cos(x) = 0 \\ x = \frac{\pi}{2} + \pi \: k \: \\ \sqrt{2} \cos(x) + 1 = 0 \\ \cos(x) = - \frac{ \sqrt{2} }{2 } \\ x = \frac{3\pi}{4} + 2\pi \: k \: \\ x = - \frac{3\pi}{4} + 2\pi \: k$