The cosine addition formula calculates the cosine of an angle
that is either the sum or difference of two other angles. It
arises from the law of cosines and the distance formula. By
using the cosine addition formula, the cosine of both the sum
and difference of two angles can be found with the two angles'
sines and cosines. I want to derive the cosine of a difference
formula but let me explain what that means first. Let's take a
look at a picture, this is the unit circle and I have two points
a and b and the coordinates of point a are cosine alpha, sine
alpha, coordinates of point b are cosine beta, sine beta. I'm
interested in finding a formula for the cosine of this angle
here beta minus alpha this angle is beta this is alpha so this
angle between the two is beta minus alpha I want a cosine for
that. Now let's recall the law of cosines, if I have a triangle
and I want to find the length of side c, I need these two sides
and the angle between them and I'll use this formula a squared
minus b squared minus 2a