When formally proving trig identities using algebra are you allowed to divide? Ordinarily I wouldn't think twice about this. Sure, the trig function by which you are dividing might take on 0, but not for all angles. We divide by potential zeros all the time.
My advisor was being very coy about the answer and it was kind of obnoxious. I know that in some constructions of the rational numbers from the integers you can't formally "divide" because, given the integers, you can't define it as an operation.
Is the trig "issue" related? I can't find anything on Google so I think he's being overly Socratic.