证明:
sina/(1+cosa)
=2sin(a/2)cos(a/2)/(1+2cos²(a/2)-1)
=2sin(a/2)cos(a/2)/(2cos²(a/2))
=sin(a/2)/cos(a/2)
=tan(a/2)
(1-cosa)/sina
=[1-(1-2sin²(a/2))]/[2sin(a/2)cos(a/2)]
=2sin²(a/2)/[2sin(a/2)cos(a/2)]
=sin(a/2)/cos(a/2)
=tan(a/2)
∴tan(a/2)=sina/(1+cosa)=(1-cosa)/sina