$$\lim_{x \to 0}\frac{\cos 2x-1}{\cos x-1}$$ I have found the above limit using L'Hopital's rule but since this rule is not given in the book so I'm supposed to do it without using this rule.
I know $$\lim_{x \to 0}\frac{1-\cos x}{x}=0$$
I tried to get something of the form of the above limit but I failed to do so.
Kindly help me solve this problem without using L'Hopital's rule.