求证:sin^3 α/(cosα+sinα)+cos^2 α/(1+tanα)=1-sinα cosα.
左边可变化为
sin^3 α/(cosα+sinα)+cos^3 α/(cosα+sinα)
若二边同乘以(cosα+sinα),
左边为sin^3 α+cos^3 α
右边=(sin^2 α+cos^2 α-sinα cosα)*(cosα+sinα)
=sin^2 αcosα+sin^3 α+cos^3 α+cos^2 αsinα-sinαcos^2 α-sin^2 αcosα
=sin^3 α+cos^3 α