More son has a nice Blog called Abstract Mathematics and Friends. The “friends” are other interests of his like computer code, esolangs, cryptography, program golfing, etc.

Here is his latest post that derives the half-angle and sum/difference trig identities using basic multiplication rules.

It is a fun article, and I think you would enjoy it. Give it a try and like/follow his blog for more in the future.

-Darren

https://wp.me/p84hnW-4z