求证tana/2=sina除以1+cosa=1-cosa除以sina

sina/(1+cosa)=[2sin(a/2)*cos(a/2)]/[1+cos²(a/2)-sin²(a/2)]
=[2sin(a/2)*cos(a/2)]/[2cos²(a/2)]
=sin(a/2)/cos(a/2)
=tan(a/2)
(1-cosa)/sina={1-[cos²(a/2)-sin²(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)
所以得证……………………………………………………
就是反复利用半倍角公式：sin2a=2sinacosa,cos2a=cos²a-sin²a