求证tan(3a/2)-tan(a/2)=【2sin(a/2)】/【cos(3a/2)】

问题描述:

求证tan(3a/2)-tan(a/2)=【2sin(a/2)】/【cos(3a/2)】

tan(3a/2)-tan(a/2)
=sin(3a/2)/cos(3a/2)-sin(a/2)/cos(a/2)
=[sin(3a/2)cos(a/2)-sin(a/2)cos(3a/2)]/[cos(3a/2)*cosa]
=sina/[cos(3a/2)*cos(a/2)]
=2sin(a/2)cos(a/2)/[cos(3a/2)*cos(a/2)]
=【2sin(a/2)】/【cos(3a/2)】
得证