Question

Помогите решить систему уровнений плиззз​

Answer 1

Ответ:

$x + y = \frac{\pi}{3} \\ \cos(x) - 2\cos(y) = 0 \\ \\ x = \frac{\pi}{3} - y \\ \cos(x) - 2 \cos(y) = 0 \\ \\ \cos( \frac{\pi}{3} - y) - 2 \cos(y) = 0$

$\cos( \frac{\pi}{3} ) \cos(y) + \sin( \frac{\pi}{3} ) \sin(y) - 2 \cos(y) = 0 \\ \frac{1}{2} \cos(x) + \frac{ \sqrt{3} }{2} \sin(y) - 2 \cos(y) = 0 \\ \frac{ \sqrt{3} }{2} \sin(y) - \frac{3}{2} \cos(y) = 0 \\ \sqrt{3} \sin(y) - 3 \cos(y) = 0 \\ \sqrt{3} \sin(x) = 3 \cos(y) \\ | \div \cos(y) \\ \sqrt{3} tgy = 3 \\ tgy = \sqrt{3} \\ y = \frac{\pi}{3} + \pi \: n$

$x = \frac{\pi}{3} - \frac{\pi}{3} + \pi \: n = \pi \: n$

n принадлежит Z.