sinα+cosα=m sinα-cosα=?

(sinα+cosα)^2=(sinα)^2+2sinαcosα+(cosα)^2=1+2sinαcosα=m^2
∴2sinαcosα=m^2-1
(sinα-cosα)^2=(sinα)^2-2sinαcosα+(cosα)^2=1-2sinαcosα=1-(m^2-1)
得,(sinα-cosα)^2=2-m^2
得,sinα-cosα=±√（2-m^2）