## Precalculus (6th Edition)

$\sin^3\theta=\sin\theta-\cos^2\theta\sin \theta$
Start with the right side: $\sin\theta-\cos^2\theta\sin \theta$ Factor out $\sin \theta$: $=\sin\theta(1-\cos^2\theta)$ Simplify: $=\sin\theta\sin^2\theta$ $=\sin^3\theta$ Since this equals the left side, the identity has been proven.
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