Proof of Compound Angle Formula cos(A-B)

The compound angle formulacan be proved by considering the sector of the unit circle between angles from the x – axis between A and B.

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

Add comment

Security code