Another thing to consider, with derived wind components, is that generally with these computer nav systems is that the displayed headwind component is that calculated along the aircraft longitudinal axis and not actually along track, so with a large drift angle the ground speed and the wind component will not add up exactly to the TAS, the larger the drift the larger the error.
The same goes for the crosswind component it is usually that calculated at 90deg to the aircraft longitudinal axis and not 90deg to the aircraft track.
It would be easy enough for the nav computer to be programmed to to make the correct calculations but in my experience it doesn't work that way.
Regards,
BH.