Question

若4cosacosb=根号6,4sinasinb=根号2,则（1-cos4a)(1-cos4b)=?

Answer 1

（1-cos4a)(1-cos4b)=(1-1+2(sin2a)^2)(1-1+2(sin2b)^2)=4(sin2a)^2(sin2b)^2

=64(sina)^2(cosa)^2(sinb)^2(cosb)^2=64(sinasinbcosacosb)^2

=64×(6/16)×(2/16)=3