I am working on a textbook problem. The first step is to prove that
$$\lim \limits_{x \to 0} \frac{\sin x}{x} = 1$$
(which I did). The exercise goes on
Use this limit [i.e. the one above] to find $$\lim \limits_{x \to 0} \frac{1 - \cos x}{x}$$.
How can this be done? I don't really see a connection between the two...