sinα-cosα=1/2
(sinα-cosα)^2=(1/2)^2
1-2sinacosa=1/4
sinacosa=3/8
sin³α-cos³α
=(sina-cosa)(sin^2a+cos^a+sinacosa)
=1/2[(sina-cosa)^2+3sinacosa]
=1/8+3/2sinacosa
=1/8+3/2*3/8
=11/16