sinx-sin^2x=cos^2x-cosx

sinx+cosx=cos²x+sin²x
sinx+sin(π/2-x)=1
2sinπ/4*cos(x-π/4)=1
2*√2/2*cos(x-π/4)=1
cos(x-π/4)=1/√2
x-π/4=-π/4+2πn U x-π/4=π/4+2πk
x=2πn,n∈z U x=π/2+2πk,k∈z