Can one trim armpit hair so as to be able to apply deodorant better?
Although it is forbidden to shave off armpit hair, it is only prohibited to do so for reasons of beautification, but permitted to do so for medical purposes (Yoreh De’ah 182:4).
Therefore, if the hair causes you distress in preventing effective application of deodrant, it is permitted to trim the armpit hair. Trimming is also more lenient than completely shaving off, because for beauty purposes the hair is usually entirely shaved off.
See also Darchei Moshe, Yoreh De’ah 182, concerning shaving hair for somebody who is ashamed; see also Tosafos, Shabbos 50; Iggros Moshe, Yoreh De’ah 2:61; Seridei Eish Vol. 2, no. 40 — the final two sources refer to the prohibition of coloring one’s hair, and write that it is permitted for non-beauty purposes.