已知sin α-cos α＝1/2 求sin³ α-cos³ α的值

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

11/16

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