Question

求证:(cosA/(tanA/2-cotA/2))=-1/2*sinA

Answer 1

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