若cosα是锐角,sinα-cosα=1/2,则sin^3α+cos^3α=

(sinα-cosα)^2=1-2sinαcosα=0.25
sinαcosα=3/8
(sinα+cosα)^2=1+2sinαcosα=7/4
sinα+cosα=(7/4)^0.5
(sinα)^3+(cosα)^3
=(sinα+cosα)((sinα)^2+(cosα)^2-sinαcosα)
=(sinα+cosα)(1-sinαcosα)
=(5/8)*(7/4)^0.5
=(5/16)*(7)^0.5

sinα-cosα=1/2
1-2sinαcosα=1/4
sinαcosα=3/8
α是锐角，(sinα+cosα)^2=7/4
sinα+cosα=根7/2（正的）
因为sinα+cosα大于0
sin^3α+cos^3α=(sinα+cosα)*(sin^2α-sinαcosα+cos^2α)
=根7/2*（1-3/8）=5根7/16