证明：sin(α+3π/4)*cos(α+π/4)=sin[π/2+(α+π/4)]*cos(α+π/4)=cos(α+π/4)*cos(α+π/4)=cos(α+π/4)=[√2/2*(cosα-sinα)]=1/2(cosα-sinα)；
2-2sin(α+3π/4)*cos(α+π/4)=2-(cosα-sinα)=2-(cosα+sinα-2cosαsinα)=1+2cosαsinα=cosα+sinα+2cosαsinα=(cosα+sinα)；
cos^4α-sin^4α=(cosα)-(sinα)=(cosα-sinα)(cosα+sinα)=(cosα-sinα)(cosα+sinα)；
[2-2sin(α+3π/4)*cos(α+π/4)]/(cos^4α-sin^4α)=(cosα+sinα)/(cosα-sinα)(cosα+sinα)=(cosα+sinα)/(cosα-sinα)=(1+tanα)/(1-tanα)