Every college math class I took gave me a sheet with those kinds of identities on it. If I was doing the kind of work where I actually had to do calculus involving trig functions, you can bet I'd pull up a similar sheet while I was working. Sure having it memorized would be a bit faster, but that's true for far more things than I can actually memorize.
Problem is you need to remember the patterns first to be able to think "hey I know this pattern. Maybe if I look up what the identity is it will be usefull"
