Show that $\sin(2nx)=\sin((2n+1)x)\cos(x)-\cos((2n+1)x)\sin(x)$.
I have the mark scheme in front of me, but it doesn't make sense to me...
Initially, I would think that it would be a double angle identity so $\sin2\theta=2\sin\theta \cos\theta$, where $\theta$ here is $nx$ but that doesn't seem to be it. How does the cosine disappear from the solution in the mark scheme? If someone could explain every step, I'd really appreciate it.