Cosx+cosy=1 x+y=2pi (решить систему уравнений)

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