(sinx-cosx)²+(sinx-cosx)=0
(sinx-cosx)(sinx-cosx+1)=0
sinx-cosx=0/cosx
tgx=1⇒x=π/4+πn,n∈z
sinx-cosx+1=0
2sinx/2*cosx/2-cos²x/2+sin²x/2+sin²x/2+cos²x/2=0
2sin²x/2+2sinx/2*cosx/2=0
2sinx/2*(sinx/2+cosx/2)=0
sinx/2=0⇒x/2=πk⇒x=2πk,k∈z
sinx/2+cosx/2=0/cosx/2
tgx/2=-1⇒x/2=-π/4+πm⇒x=-π/2+2πm,m∈z