sinx+cosx=cos2x=(cosx)^2-(sinx)^2=(cosx+sinx)(cosx-sinx)
⇔(sinx+cosx)(cosx-sinx-1)=0
1)sinx+cosx=0
⇔√2sin(x+π/4)=0よりx=3π/4,7π/4
2)-sinx+cosx=1
⇔√2sin(x+3π/4)=1
⇔sin(x+3π/4)=1/√2よりx=0,3π/2