Question

已知sinx+cosx=m(|m|≤根号2且|m|不等于1)求1 sinx三次方+cosx三次方等于多少?

Answer 1

sinx+cosx=m 平方一下得

sin^2x+2sinxcosx+cos^2x=m^2

sinxcosx=(m^2-1)/2

sin^3x+cos^3x

=(sinx+cosx)(sin^2-sinxcosx+cos^2x)

=m(1-(m^2-1)/2)

=m(3-m^2)/2