# How do you prove 2sinthetacos^3theta+2sin^3thetacostheta=sin2theta?

Sep 18, 2016

$2 \sin \theta {\cos}^{3} \theta + 2 {\sin}^{3} \theta \cos \theta$
= $2 \sin \theta \cos \theta \left({\cos}^{2} \theta + {\sin}^{2} \theta\right)$
= $\sin 2 \theta \times 1$
= $\sin 2 \theta$