(1＋sinθ＋cosθ)/(1＋sinθ－cosθ)=[2sin(θ/2)cos(θ/2)＋2cos²(θ/2)]/[2sin(θ/2)cos(θ/2)＋2sin²(θ/2)]=cos(θ/2)/sin(θ/2).
(1－cosθ＋sinθ)/(1＋cosθ＋sinθ)=[2sin(θ/2)cos(θ/2)＋sin²(θ/2)]/[2sin(θ/2)cos(θ/2)＋2cos²(θ/2)]=sin(θ/2)/cos(θ/2).
所以,原式=cos(θ/2)/sin(θ/2)＋sin(θ/2)/cos(θ/2)=[cos²(θ/2)＋sin²(θ/2)]/[sin(θ/2)cos(θ/2)]=2/sinθ.