设A+π/6=α,则2A+π/12=2α-π/4
cosα=4/5,α为锐角,sinα=3/5,所以sin2α=2sinαcosα=24/25,cos2α=2(cosα)^2-1=7/25
sin(2A+π/12)=sin(2α-π/4)=√2/2(sin2α-cos2α)=(17√2)/50