Question

Simplify a trigonometric expression sin θ cos2 θ − sin θ

Answer 1

$sin\theta cos2\theta - sin\theta \\ \text{Recall that} \, cos2\theta = 1 - 2sin^2\theta. \text{Hence, we have}\\ sin\theta(1 - 2sin^2\theta) - sin\theta \\ = sin\theta - 2sin^3\theta - sin\theta\\ = -2sin^3\theta$