sin(a+b), cos(a+b)

sin(a+b), cos(a+b)

Hello everyone!

Today, while doing the dishes, I suddenly realized that the formulas for sin and cos of a sum can be derived via consecutive multiplication of rotation matrices. But I clearly remember that at school our teacher derived them through geometry and the Pythagorean theorem. Can anyone explain why?

P.S. I honestly think that in school sin(a+b) and cos(a+b) should just be part of the axiomatic base, but if someone does want to derive them, what is the best way to do it?