Question

Помогите решить уравнение 2 cos2 x-cos x-1=0

Answer 1

$2 { \cos(x) }^{2} - \cos(x) - 1 = 0 \\ \cos(x) = t \\ - 1 \leqslant t \leqslant 1 \\ 2 {t}^{2} - t - 1 = 0 \\ t(1) = 1 \\ t(2) = - \frac{1}{2} \\ \cos(x) = 1 \\ x = 2\pi n \\ \cos(x) = - \frac{1}{2} \\ x = \frac{2\pi}{3} + 2\pi k \\ x = \frac{4\pi}{3} + 2\pi m$