[tex]\left \{ {{x + y = \frac{Pi}{2}} \atop {sinx + cosy = \sqrt{2} }} ight[/tex]

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