已知sina sinb sinc=0,cosx cosb cosc=0,cos(a-b)=? (答案是-1/2)

热心网友

sinA+sinB+sinC=0---sinA+sinB=-sinC......(1)cosA+cosB+cosC=0---cosA+cosB=-cosC......(2)(2)^2+(1)^2:[(cosA)^2+(cosB)^2+2cosAcosB]+[(sinA)^2+(sinB)^2+2sinAsinB]=(-sinC)^2+(-cosC)^2---1+1+2(cosAcosB+sinAsinB)=1---2+2cos(A-B)=1---cos(A-B)=-1/2.