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Proof of the Compound Angle Formula for cos(A-B)

The compound angle formulacan be proved by considering the sector of the unit circle between angles from the x – axis betweenand

The coordinates ofareand the coordinates of L areThe distance,betweenandsatisfies

From the Cosine Rule

Since the circle is a unit circle,andso

Equating these two expressions gives

which simplifies to

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