α∈(0,π/2),∴u=α+π/3的值域是(π/3,5π/6),cosu=4/5,∴sinu=3/5,∴sin2u=2sinucosu=24/25,cos2u=2(cosu)^2-1=7/25,2α+5π/12=2u-π/4,∴cos(2α+5π/12)=(√2/2)cos2u+(√2/2)sin2u=31√2/50.
