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:
