求证:(cosA/(tanA/2-cotA/2))=-1/2*sinA
问题描述：
求证:(cosA/(tanA/2-cotA/2))=-1/2*sinA
答
tan(A/2)-cot(A/2)
=sin(A/2)/cos(A/2)-cos(A/2)/sin(A/2)
=[sin²(A/2)-cos²(A/2)]/cos(A/2)sin(A/2)
=-cosA/(1/2sinA)
=-2cosA/sinA
所以：
等式左边=cosA/[tan(A/2)-cot(A/2)]
=cosA/(-2cosA/sinA)
=-1/2*sinA