How do you derive the trig addition formulas?
Squaring both sides of that gives
Now, that isn't quite what we want but if we take x= a, y= a+b, we can "reverse" that: now b= y- a= y- x so that becomes
Replacing x by -x and using the fact that cosine is an even function and sine is an odd function.
sin(y+x) can be done now by using the fact that and .