Using the double angle formula, it's characteristics and applications

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:

• The answer sheet is wrong. You are correct. – drhab Dec 14 '18 at 11:23
• One more typo in a textbook ! – Claude Leibovici Dec 14 '18 at 11:27
• 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 – BM97 Dec 14 '18 at 11:49