说明：你的题目最后一个等号应该是加号,证明过程中由于打不出平方,就用★代替,√2表示根号2.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-(cos★α+sin★α-2cosαsinα)=1+2cosαsinα=cos★α+sin★α+2cosαsinα=(cosα+sinα)★；cos^4α-sin^4α=(cos★α)★-(sin★α)★=(cos★α-sin★α)(cos★α+sin★α)=(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)