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