I saw these trig identities at the beginning of this video on PatrickJMT » Trigonometric Integrals – Part 5 of 6 and I don't remember using these identities before. They weren't in the back of my textbook either. Does anyone know what they're called, and maybe a simple method for deriving them? And by simple I mean along the lines of deriving a half-angle formula using Pythagorean theorem and double-angle formulas. It doesn't have to be simple, I'm just hoping there's a simple way to memorize them!

Here's the identities if the link doesn't work:

Edit: I just realize this might be better of in the Trig forum and not calculus. I posted here just out of habit! And fix't the typos