Problems in verifying trigonometric identities are famous in nearly all pure mathematics courses, and usually it is taught as a game of manipulating both sides of the propositioned identity with the body of known trig identities until the LHS = RHS.
I wanted to know if there were other approaches to proving trigonometric identities too. I did some google searches and found there are “inductive” methods of proof as opposed to “deductive” (which is how we’ve been approaching the problem of proving trig identities) although it looks like that method is reserved for integers so not very helpful here