How do you prove $2 sin θ {cos}^{3} θ + 2 {sin}^{3} θ cos θ = sin 2 θ$ $2sinthetacos^3theta+2sin^3thetacostheta=sin2theta$ ?

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Answer 1 · 2016-09-18T05:13:50

Please see below.

$2 sin θ {cos}^{3} θ + 2 {sin}^{3} θ cos θ$ $2sinthetacos^3theta+2sin^3thetacostheta$

= $2 sin θ cos θ ({cos}^{2} θ + {sin}^{2} θ)$ $2sinthetacostheta(cos^2theta+sin^2theta)$

= $sin 2 θ \times 1$ $sin2thetaxx1$

= $sin 2 θ$ $sin2theta$

How do you prove 2sinthetacos^3theta+2sin^3thetacostheta=sin2theta2sinθcos3θ+2sin3θcosθ=sin2θ2sinthetacos^3theta+2sin^3thetacostheta=sin2theta?