∠A是锐角,根据cos(A+π/6)=4/5,∠A+π/6<π/2,∠A<π/3,所以sin(A+π/6)=3/5,sin(2A+π/3)=2sin(A+π/6)cos(A+π/6)=24/25,2A+π/3<π,cos(2A+π/3)=7/25,sin(2A+π/12)=sin(2A+π/3-π/4)=sin(2A+π/3)cos(π/4)-cos(2A+π/3)sin(π/4)=24/25×√2/2-7/25×√2/2=17√2/50