已知sinx-cosx=1/3,求sin2x sin^3x-cos^3x
问题描述：
已知sinx-cosx=1/3,求sin2x sin^3x-cos^3x
答
sinx-cosx=1/3
(sinx-cosx)^2=1/9
2sinxcosx=8/9
sin2x=8/9
sin^3 x - cos ^3 x=(sinx-cosx)(sin^2x+sinxcosx+cos^2x)
=1/3 * (1+4/9)
=13/27
答
(sinx-cosx)^2=(sinx)^2-2sinxcosx+(cosx)^2=1-sin(2x)=1/9
sin(2x)=1-1/9=8/9
(sinx)^3-(cosx)^3
=(sinx-cosx)[(sinx)^2+sinxcosx+(cosx)^2]
=(1/3)[1+sin(2x)/2]
=(1/3)(1+4/9)
=13/27