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So I know the double angle formula is

$$ 2 \sin \alpha \cos \alpha = \sin(2\alpha) $$

I have this equation :

$$ 2\sin(mx+ny)(\cos(mx+ny))m $$

Now according to the answers sheet if I use the double angle formula I get

$$ 2m\sin(2mx + 2ny) $$

But according to the formula, wouldn't I have to multiply only $\alpha$ by $2$?

According to me, I would get

$$ sin(2mx+2ny)m, ~~\text{without the 2 upfront.} $$

Can somebody please explain what I'm doing wrong? Or what I'm not understanding correctly?

Does the formula

$$ 2 \sin \cos\alpha \cos \alpha = \sin(2\alpha) ~~~\text{imply}~~ 2\sin(2\alpha) ~~~\text{?}$$

A photo of the problem for reference: enter image description here

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    $\begingroup$ The answer sheet is wrong. You are correct. $\endgroup$ – drhab Dec 14 '18 at 11:23
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    $\begingroup$ One more typo in a textbook ! $\endgroup$ – Claude Leibovici Dec 14 '18 at 11:27
  • $\begingroup$ Thanks ! May you please check the picture that i uploaded and still tell me if im right? Maybe i'm missing something or i dont know $\endgroup$ – BM97 Dec 14 '18 at 11:49

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