若cos x-sin x = 0.5,则cos^3 x-sin^3 x =

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/10 12:48:34
若cosx-sinx=0.5,则cos^3x-sin^3x=若cosx-sinx=0.5,则cos^3x-sin^3x=若cosx-sinx=0.5,则cos^3x-sin^3x=将cosx-sinx

若cos x-sin x = 0.5,则cos^3 x-sin^3 x =
若cos x-sin x = 0.5,则cos^3 x-sin^3 x =

若cos x-sin x = 0.5,则cos^3 x-sin^3 x =
将cosx-sinx=0.5两边平方得到cos^2 x+sin^2 x-2sinxcosx=0.25
于是sinxcosx=0.375
而cos^3 x-sin^3 x通过立方差公式分解后得到:
(cosx-sinx)(cos^2 x+sinxcosx+sin^2 x)
=0.5*(1+0.375)
=0.5*1.375
=0.6875