令x+y=A,x-y=Bcos(x+y)cos(x-y)= cosAcosBx=(A+B)/2,y=(A-B)/2,代入cos^2(x)-sin^2(y)=cos2(A+B/2)-sin2(A-B/2)=[1+cos(A+B)-1+cos(A
-B）]/2=cosAcosB-sinAsinB+cosAcosB+sinAsinB）/2=cosAcosB所以cos(x+y)cos(x-y)= cos2x-sin2y