cos2α/tan(π/4+α)
=sin(π/2+2α)/tan(π/4+α)
=2sin(π/4+α)cos(π/4+α)/[sin(π/4+α)/cos(π/4+α)]
=2cos^2(π/4+α)
=2[1+cos(π/2+2α)]/2
=1-sin2α