\begin{equation*}
\begin{split}
& \lim_{x\rightarrow 0} \frac{\cos x-\cos 3x}{1-\cos 2x} \\\\
& \lim_{x\rightarrow 0} \frac{-2 \sin \frac 12 (x + 3x) \sin \frac 12 (x - 3x)}{1- (1 - 2 \sin^2 x)} \\\\
& \lim_{x\rightarrow 0} \frac{-2 \sin 2x \sin (-x)}{1- 1 + 2 \sin^2 x} \\\\
& \lim_{x\rightarrow 0} \frac{2 \sin 2x \sin x}{2 \sin^2 x} \\\\
& 2
\end{split}
\end{equation*}