СИСТЕМА: X+Y=п/2 И sin^2x -sin^2y=1

Question

СИСТЕМА: X+Y=п/2 И sin^2x -sin^2y=1

Answer 1

Y=π/2-x
siny=sin(π/2-x)=cosx

x+y=π/2
sin²x-sin²y=1  или  sin²x-cos²x=-(cos²x-sin²x)= - cos2x=1

cos2x= -1    2x=π+2πk    
x=π/2+πk   k∈Z
y=π/2-π/2-πk = -πk   k∈Z