已知sinx+cosx=1/3,求sin^3x+cos^3x

问题描述:

已知sinx+cosx=1/3,求sin^3x+cos^3x

由 (sinx+cosx)^3 = (sinx)^3+(cosx)^3 + 3sinxcosx(sinx+cosx)得 (sinx)^3+(cosx)^3 = (sinx+cosx)^3 - 3sinxcosx(sinx+cosx)= (1/3)^3-3*(1/3)sinxcosx= 1/27-sinxcosx (1)又由 sinx+cosx=1/3 得 (sinx+cosx)^2=(1...