sinα+cosα=√2(sinαcos(π/4)+cosαsin(π/4))=√2sin(α+π/4)>0
则可得α+π/4∈（0+2kπ,π+2kπ）,则α的取值范围是（-π/4+2kπ,3π/4+2kπ）
sinα -cosα=√2(sinαcos(π/4)-cosαsin(π/4))=√2sin(α-π/4)