已知sinx+cosx=m,则sin立方x+cos立方x的值为

(sinx)^3+(cosx)^3
=(sinx+cosx)[(sinx)^2-sinxcosx+(cosx)^2]
=m(1-sinxcosx)
又因为（sinx+cosx）=m^2=1+2sinxcosx
所以sinxcosx＝(m^2-1)/2
原式＝m{1-[(m^2-1)/2]}
=m(1-m^2/2+1/2)
=m[(3/2)-(m^2/2)}
=3m/2-m^3/2
=(3m-m^3)/2