Question

Решите систему тригонометрических уравнений x-y=п cos(x)-cos(y)=корень из 3

Answer 1

Ответ:

$\left \{ {{x - y = \pi} \atop { \cos(x) - \cos(y) = \sqrt{3} } } \right. \\ \\ \left \{ {{x = y + \pi} \atop { \cos(x) - \cos(y) = \sqrt{3} } } \right. \\ \\ \cos( y + \pi) - \cos(y) = \sqrt{3} \\ - \cos(y) - \cos(y) = \sqrt{3} \\ - 2 \cos(y) = \sqrt{3} \\ \cos(y) = - \frac{ \sqrt{3} }{2} \\ y = \pm \frac{5\pi}{6} + 2\pi \: n \\ \\ y1 = \frac{5\pi}{6} + 2 \pi \: n \\ x1 = \frac{5\pi}{6} + \pi + 2\pi \: n = \\ = \frac{11\pi}{6} + 2\pi \: n \\ \\ y2 = - \frac{5\pi}{6} + 2\pi \: n \\ x2 = - \frac{5\pi}{6} + \pi + 2\pi \: n = \\ = \frac{\pi}{6} + 2 \pi \: n$

n принадлежит Z.