limit of ${\displaystyle \frac{1-cosx}{x}}$ as $x$ approaches 0

Corollary 1.

$$\underset{x\to 0}{lim}\frac{1-\cos x}{x}=0$$

Proof.

This corollary has an obvious corollary to it:

Corollary 2.

$$\underset{x\to 0}{lim}\frac{\cos x-1}{x}=0$$