[latex] \left \{ {{cosx+cosy=1} \atop {x+y=2}} \right. [/latex] решите систему уравнений

x+y=2рi             x=2pi-y cosx+cosy=1 cos(2pi-y)+cosy=1  2cosy=1  cosy=1/2  y=+-П/3+2Пk x=2П+-П/3+2Пk  x=5п/3+2Пk  x=7П/3+2Пk

[latex] \left \{ {{cosx+cosy=1} \atop {x+y=2 \pi }} \right. \left \{ {{cos(2 \pi -y)+cosy=1} \atop {x=2 \pi -y}} \right. \left \{ {{2cosy=1} \atop {x=2 \pi -y}} \right. \left \{ {{cosy= \frac{1}{2} } \atop {x=2 \pi -y}} \right. \left \{ {{y= -\frac{ \pi }{3}+2 \pi n ;y= \frac{ \pi }{3}+2 \pi n } \atop {x=\frac{ 7\pi }{3}-2 \pi n } ;x= \frac{5 \pi }{3}-2 \pi n } \right. [/latex]