若cos x-sin x = 0.5,则cos^3 x-sin^3 x =
问题描述：
若cos x-sin x = 0.5,则cos^3 x-sin^3 x =
答
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...