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How would I prove the following identity?

$\sin x=2\sin\frac{x}{2}\cos\frac{x}{2}$

I know $\sin(a+b)=\sin a\cos b+\sin a \cos b.$

So I did

$\sin\frac{x}{2}\cos\frac{x}{2}+\cos\frac{x}{2}\sin\frac{x}{2}.$

But what technique would I have to use to continue the problem?

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    Is there a tutorial for this latex I think someone posted a link once....2012-07-28

1 Answers 1

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Since $\sin(a+b) = \sin a \cos b + \cos a \sin b$, letting $a = b = \frac{x}{2}$ gives $\sin x = \sin \frac{x}{2} \cos \frac{x}{2} + \cos \frac{x}{2} \sin \frac{x}{2} = 2 (\sin \frac{x}{2} \cos \frac{x}{2})$.

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    Oops, I missed that :-).2012-07-28