已知cos(α+π/6）=4/5, 求sin（2α+π/12）设α+π/6=β,则α=β-π/6,cosβ=4/5,故sin(2α+π/12)=sin[2(β-π/6)+π/12]=sin(2β-π/4)=(√2/2)(sin2β-cos2β)=(√2/2)[2sinβcosβ-(2cos²β-1)]=(√2/2)(2...