"Someone may be displaying anger from the outside, yet underneath anger could be hidden sadness."

Yes.

On the other hand, it has been my experience doing emotional release work with people that it is often sadness that is the surface "presenting" emotion which covers up an unfelt and never expressed anger. This is especially true of people who have felt powerless in a situation where displaying anger would have been unaccepted. Everyone will accept that you might be sad, but there are many situations where anger would not be tolerated (your job? your family? your group of friends? etc.). "I can sympathize with your sadness. I will not tolerate your anger" reacts some long since internalized unconscious mechanism.