Question

$left { {{x + y = frac{Pi}{2}} atop {sinx + cosy = sqrt{2} }} right$

Answer 1

 

 

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