Vibrations and Waves · Problem 1-8

The superposition of periodic motions — A.P. French

Physics — Waves · complex-exponential-trigonometric-identities

Problem

Using the exponential representations for

\sin\theta

and

\cos\theta

, verify the following trigonometric identities: (a)

\sin^2\theta + \cos^2\theta = 1

(b)

\cos^2\theta - \sin^2\theta = \cos 2\theta

(c)

2\sin\theta\cos\theta = \sin 2\theta