“化简( tan3/2x-tanx/2)(cosx+cos2x)/sinx”

tan(3x/2)-tan(x/2) = [sin(3x/2)/cos(3x/2) - sin(x/2)/cos(x/2)]
= (sin3x/2 cosx/2 - con3x/2 sinx/2) / cos3x/2 cosx/2
其中：(sin3x/2 cosx/2 - con3x/2 sinx/2) = [(sin2x+sinx)-(sin2x-sinx)]/2 = sinx
所以：tan(3x/2)-tan(x/2) = sinx/(cos3x/2 cosx/2)
又：cosx+cos2x = 2cos3x/2 cosx/2
所以原式分子= 2sinx 原式=2