# Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Concept and Vocabulary Check - Page 679: 1

The required value of the sin 2x is 2 sin x cos x.

#### Work Step by Step

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.

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