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 $\cos(t)$.

It depends how you classify simpler. One possibility is:
$$2\cos t\cos 2t-\sin t\sin 2t=\frac{3}{2}\cos t\cos 2t-\frac{3}{2}\sin t\sin 2t+\frac{1}{2}\cos t\cos 2t+\frac{1}{2}\sin t\sin 2t$$
$$=\frac{1}{2}\big(3(\cos t\cos2t-\sin t\sin 2t)+(\cos t\cos 2t+\sin t\sin 2t)\big)$$
$$=\frac{1}{2}\left(3\cos 3t+\cos t\right)$$
This does make use of the formula you were referencing.
