sin(π/4+α)=cos[π/2-(π/4+α)]=cos(π/4-α)
tan(π/4-α)=sin(π/4-α)/cos(π/4-α)
所以分母=2cos²(π/4-α)*sin(π/4-α)/cos(π/4-α)
=2sin(π/4-α)cos(π/4-α)
=sin[2(π/4-α)]
=sin(π/2-2α)
=cos2α
分子=cos2α
所以原式=1