Question

Система уравнений:

cos(y)*cos(x)=-0.25
tg(y)=ctg(x)

Буду очень признательна <3

Answer 1

Ответ:

$cosy \times cosx = - \frac{1}{4} \\ \frac{siny}{cosy} = \frac{cosx}{sinx} = > \\ sinx \times siny = - \frac{1}{4}$

$cosy \times cosx = - \frac{1}{4} \\ sinx \times siny = - \frac{1}{4} \\ cos(x + y) = - \frac{1}{4} - ( - \frac{1}{4} ) = 0 \\ x + y = \frac{\pi}{2} = > y = \frac{\pi}{2} - x$

$cos( \frac{\pi}{2} - x) \times cosx = - \frac{1}{4} \\ 2(cosx \times sinx) =2 \times ( - \frac{1}{4} ) \\ sin2x = - \frac{1}{2} \\ 2x = - \frac{\pi}{6} \\ x = - \frac{\pi}{12} \\ y = \frac{\pi}{2} + \frac{\pi}{12} = \frac{7\pi}{12}$

$x = - \frac{\pi}{12} \\ y = \frac{7\pi}{12}$