#### Answer

$\sin^3\theta=\sin\theta-\cos^2\theta\sin \theta$

#### Work Step by Step

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.