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