I'm trying to follow the answer from this question – Verifying $\sin 4θ=4\cos^3 θ \sin θ – 4\cos θ \sin^3θ$
and I'm referencing the trig identities from the Khan academy website here – https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference
but I'm having trouble finding out how the equation $4\sin θ\cos θ(\cos^2θ−\sin^2θ)=2\sin(2θ)\cos(2θ)$ is solved.
Best Answer
\begin{align} \sin4\theta&=2\color{blue}{\sin2\theta}\color{red}{\cos2\theta}\\ &=2(\color{blue}{2\sin\theta\cos\theta})(\color{red}{\cos^2\theta-\sin^2\theta})\\ &=4\sin\theta\cos\theta(\cos^2\theta-\sin^2\theta) \end{align}
Does this help?