How to derive the formula cos(A+B) from the formula cos(A-B)? How do I derive the formula:
cos(A+B)=cosAcosB-sinAsinB 
from the formula:
cos(A-B)=cosAcosB+sinAsinB? 
The only difference that I noticed is the negative and positive sign. I was thinking that first, I replace B with (-B), but then after that how does cos(-B) turn to cos(B), and sin(-B) turn to -sin(B)?
Thank you, can someone please explain to me. I hope my question was not too confusing.

$$\cos (A-(-B)) = \cos A \cos -B + \sin A \sin -B = \cos A \cos B - \sin A \sin B= \cos (A+B)$$
Based on the even odd properties of $\sin $ and $\cos $
