Answer
See the step-by-step proof below.
Work Step by Step
As shown in the figure in the book, coordinates of C and D on the unit circle are:
$ C(cosA,sinA)$ and $ D(cosB,sinB)$
The distance between C and D is: $\sqrt {(cosA-cosB)^2+(sinA-sinB)^2}$
Based on the cosines law, we have:
$(cosA-cosB)^2+(sinA-sinB)^2=1^2+1^2-2cos(A-B)$
Using the identities $ sin^2A+cos^2A=1$ and $ sin^2B+cos^2B=1$, we can rewrite the above as:
$ cos(A-B)=cosAcosB+sinAsinB $
