x+y=pi/2
sin(x)+cos(y)=sqrt(2)
x=(pi/2)-y
sin((pi/2)-y)+cos(y)=sqrt(2)
cos(y)+cos(y)=sqrt(2)
2cos(y)=sqrt(2)
cos(y)=sqrt(2)/2
y=±arccos(sqrt(2)/2)+2pi*n
y=±(pi/4)+2pi*n
x=(pi/2)-y=(pi/2)±pi/4+2pi*n
Ответ:
x=(pi/2)-y=pi/4+2pi*n
y=(pi/4)+2pi*n
и
x=3pi/4+2pi*n
y=-(pi/4)+2pi*n