(1+sinθ+cosθ)/[sin(θ/2)+cos(θ/2)]
=[2cos²(θ/2)+2sin(θ/2)cos(θ/2)]/[sin(θ/2)+cos(θ/2)]
=2cos(θ/2)[sin(θ/2)+cos(θ/2)]/[sin(θ/2)+cos(θ/2)]
=2cos(θ/2)