Система уравнения sinx+cosy=1 х+у=2п

Question

Система уравнения sinx+cosy=1 х+у=2п

Answer 1

X=2π-y
sinx+cosy=1
sin(2π-y)+cosy=1
-siny+cosy=1
-siny+sin(π/2-y)=1
2sin(π/4-y)cosπ/4=1
√2sin(π/4-y)=1
cos(π/4+y)=1/√2
π/4+y=-π/4 U π/4+y=π/4
y1=-π/2 U y2=0
x1=2π+π/2=3π/2 U x2=2π-0=2π