Система: sin(x-y)=2sinxsiny x+y=п/2

X=π/2-y

sin(π/2-2y)=2sin(π/2-y)*cosy
-cos2y=2cos²y
2cos²у+cos2y=0
2cos²у+2cos²у-1=0
4cos²у=1
cos²у=1/4

cosу=1/2 или cosу=-1/2
для cosy=1/2

y1=π/3+2πn, n € Z
y2=-π/3+2πn, n € Z

для cos y=-1/2
y3=2π/3+2πn, n € Z
y4=-2π/3+2πn, n € Z

x1=π/2-π/3+2πn=π/6+2πn, n € Z
x2=π/2+π/3+2πn=5π/6+2πn, n € Z
x3=π/2-2π/3+2πn=-π/6+2πn, n € Z x4=π/2+2π/3+2πn=7π/6+2πn, n € Z