MHB Easy Identity Question: Proving 2cos(x)sin(x) = sin(2x)

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The identity 2cos(x)sin(x) = sin(2x) is confirmed as correct. The discussion highlights the importance of proper notation in trigonometric expressions, recommending the use of either $\sin x$ or $\sin(x)$ instead of sinx. It emphasizes that when combining functions, parentheses should be used to clarify the argument. The mention of double-angle formulas indicates a resource for further exploration of trigonometric identities. Proper notation is essential for clear mathematical communication.
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Hi,

I just want to double check that

2cos(x)sin(x) = 2sin(x)cos(x) = sin(x)2cos(x) = sin(2x)

Thanks,

Tim
 
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Yes. the identity is correct. You can find a list of trigonometric identities in Wikipedia. See, in particular, double-angle formulas.

A couple of remarks about notation. One should write $\sin x$ (with a space) or $\sin(x)$, not sinx. If the argument is followed by another factor, then the argument should be wrapped in parentheses. For example, $\sin x\cos x$ can theoretically be parse either as $\sin(x)\cos(x)$ or as $\sin(x\cos(x))$, but $\sin(x)\cos(x)$ clearly shows that the argument of sine is just $x$.
 
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