Question

已知sinx+cosx=m,则sin立方x+cos立方x的值为

Answer 1

(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...