Cosine of B - A

Rotate the angle down until B-A is in standard position. Notice that there are two different ways of calculating the length of the chord (squared) as you see in the lower left of the applet.

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If you FOIL out the squares in the equation, and cancel stuff, and use the Pythagorean Identity, you get:
cos(B)^2 + cos(A)^2 - 2*cos(B)cos(A) + sin(B)^2 + sin(A)^2 - 2*sin(B)sin(A) = cos(B-A)^2 - 2cos(B-A) + 1 + sin(B-A)^2

2 - 2cos(B)cos(A) - 2sin(B)sin(A) = 2 - 2cos(B-A)

Switching sides and canceling 2's all over, you get:

cos(B-A) = cos(B)cos(A) + sin(B)sin(A)

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