## Precalculus (6th Edition) Blitzer

In order to find the value of sin 2x, the double angle formula is used that is as shown below: $Sin\left( \alpha +\beta \right)=\sin \alpha \,\cos \beta +\cos \alpha +\,\sin \beta$ Now, consider $\alpha$ and $\beta$ as x in sin (x+x); then the formula becomes: \begin{align} & Sin\left( x+x \right)=\sin x\,\cos x+\cos x\,\sin x \\ & sin\,2x=2\,\sin x\,\cos x \end{align} Hence, the required value of the sin 2x is 2 sin x cos x.