What Trig Identity are these?

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

Re: What Trig Identity are these?

I believe you have mis-written these identities; they should be:

These can all be derived from the basic identities:

,

For example:

The other two can be derived in similar fashion.

Re: What Trig Identity are these?

Hello, AZach!

Careful! . . . Your identities have terrible typos.

Product-to-Sum Indentities

. .

Sum-to-Product Identities

. .

These are lesser-known identities,

. . but become more important later on.