Prerequisite for addition formula: https://www.youtube.com/watch?v=iHZmi2MHqWc
Proof of formula for sin(A+B): https://www.youtube.com/watch?v=BEETggUVMrY
Proof of formula for cos(A+B): https://www.youtube.com/watch?v=gTpNnlRxnIY
Proof of formula for tan(A+B): https://www.youtube.com/watch?v=D5VJiL0DMWU
Some C3 Trig stuff: https://www.youtube.com/watch?v=Gcby6WYAVKg
The product rule proof with limits:https://www.youtube.com/watch?v=9FRFRVTUthk