Question

Решить уравнение 2cos( x-1)=-1

Answer 1

$2\cos (x - 1) = -1$

$\cos(x - 1) = -\dfrac{1}{2}$

$x - 1 = \pm \arccos \left(-\dfrac{1}{2} \right) + 2\pi n, \ n \in Z$

$x - 1 = \pm \left(\pi - \arccos\dfrac{1}{2} \right) + 2\pi n, \ n \in Z$

$x - 1 = \pm \left(\pi - \dfrac{\pi}{3} \right) + 2\pi n, \ n \in Z$

$x - 1 = \pm \dfrac{2\pi}{3} + 2\pi n, \ n \in Z$

$x = 1 \pm \dfrac{2\pi}{3} + 2\pi n, \ n \in Z$

Ответ: $x = 1 \pm \dfrac{2\pi}{3} + 2\pi n, \ n \in Z$