∵sin(7/12π+α)=2/3,
α-11/12π=-3π/2+(7π/12+α)
∴cos(α-11/12π)
=cos[-3π/2+(7π/12+α)]
=cos[-3π/2+2π+(7π/12+α)]
=cos[π/2+(7π/12+α)]
=-sin(7π/12+α)
=-2/3