Given this formula

Sum

sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b)

prove this one

Difference

sin(a-b)=sin(a)*cos(b)-cos(a)*sin(b)

Given this formula

Sum

cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)

prove this one

Difference

cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)

I assume it's the same concept for both of them, i just don't know how to go about proving it to be true.