已知4xinAsinB=3 4cosAcosB=1求(1-4cos4A)(1-4cos4B)

4sinAsinB=3,4cosAcosB=1
sinAsinB=3/4,cosAcosB=1/4
cosAcosB+sinAsinB=cos(A-B)=1 sin(A-B)=0
cosAcosB-sinAsinB=cos(A+B)=-1/2
cos4A=2(cos2A)^2-1
cos4B=2(cos2B)^2-1
cos2A=cos[(A+B)+(A-B)]=cos(A+B)cos(A-B)-sin(A+B)sin(A-B)=-1/2
cos2B=cos[(A+B)-(A-B)]=cos(A+B)cos(A-B)+sin(A+B)sin(A-B)=-1/2
(1-cos4A)(1-cos4B)=3/2*3/2=9/4