I generally just know that any trig formula can be converted to quite a few different other ones visa trig identities. Whether a certain expression is more or less complex than another is a matter of perspective and context.

If I'm stuck with a trig function I don't know what to do with, I just look on Wikipedia for a trig identity and don't worry about derivations or memorization.

This trick is good for exam settings though! My memory is terrible so I always relied on tricks like this in school