tan3x/2-tanx/2
=(sin3x/2)/(cos3x/2) - (sinx/2)/(cosx/2)
=(sin3x/2*cosx/2 - sinx/2 * cos3x/2 )/(cos3x/2*cosx/2)
=sin(3x/2 - x/2)/[1/2(cos(3x/2+x/2)+cos(3x/2-x/2)]
=2sinx/(cos2x+cosx)