`B=(sinalpha-2sin2alpha+sin3alpha)/(cosalpha-2cos2alpha+cos3alpha)`

`=((sinalpha+sin3alpha)-2sin2alpha)/((cosalpha+cos3alpha)-2cos2alpha)`

`=(2sin((alpha+3alpha)/2) .cos((alpha+3alpha)/2)-2sin2alpha)/(2cos((alpha+3alpha)/2) .cos((alpha+3alpha)/2)-2cos2alpha)`

`=(2sin2alpha cosalpha-2sinalpha)/(2cos2alpha cosalpha-2cos2alpha)`

 `=(sin2alpha.(2cosalpha-2))/(cos2alpha.(2cosalpha-2))` $\\$ `=(sin2alpha)/(cos2alpha)`

`=tan2alpha`