Simplifying $2\cos(t)\cos(2t)-\sin(t)\sin(2t)$ How do I simplify $2\cos(t)\cos(2t)-\sin(t)\sin(2t)$? I know this should be possible, but I don't know how.
I have tried the $\cos(t)\cos(u)-\sin(t)\sin(u)=\cos(t+u)$, but I don't know what to do with the $2$ in front of $\cos(t)$.

You said it yourself, but were confused what to do with the 2:
$$2\cos{(t)}\cos{(2t)}=\cos{(t)}\cos{(2t)}+\cos{(t)}\cos{(2t)}$$
So then your expression becomes
$$\cos{(t)}\cos{(2t)}+\left[\cos{(t)}\cos{(2t)}-\sin{(t)}\sin{(2t)}\right]$$
Now simplify the bracketed expression to $\cos{(3t)}$ by your identity and you have
$$2\cos{(t)}\cos{(2t)}-\sin{(t)}\sin{(2t)}=\cos{(t)}\cos{(2t)}+\cos{(3t)}$$
