已知sin α-cos α=1/2 求sin³ α-cos³ α的值

问题描述:

已知sin α-cos α=1/2 求sin³ α-cos³ α的值

(sin α-cos α)^2=(sina)^2-2sinacosa+(cos)^2=1-2sinacosa=1/4sinacosa=3/8(sina)^3-(cosa)^3=(sina-cosa)[(sina)^2+sinacosa+(cos)^2]=1/2(1+sinacosa)=1/2(1+3/8)=11/16