Question

Решить тригонометрическое уравнение

Answer 1

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