Система x+y=pi sinX+siny=-корень из 2

Question

Система
x+y=pi
sinX+siny=-корень из 2

Answer 1

SinX+sinY=2*sin((x+y)/2)*cos((x-y)/2)=2*sin(PI/2)*cos((x-y)/2)=-sqrt(2);
cos((x-y)/2)=-sqrt(2)/2
(x-y)/2=3/2*pi
x-y=3*pi

x+y=pi
x-y=3pi

2x=4pi; x=2pi
y=-pi