sinα+cosα=根号2,求sin3次方α+cos三次方α及sin4次方α+cos4次方α

sinα+cosα=根号2
（sinα+cosα）^2=2
sinαcosα=1/2
sin^3α+cos^3α
=(sinα+cosα)(sin^2α+cos^2α-sinαcosα)
=√2/2
sin^4α+cos^4α
=(sin^2α+cos^2α)^2-2(sinαcosα)^2
=1-1/2=1/2