Question

Evaluate $\underset{x\to 0}{lim}\frac{\cos 2x-1}{\cos x-1}$

Answer 1

Let

$L={lim}_{x\to 0}\frac{\cos 2x-1}{\cos x-1}={lim}_{x\to 0}\frac{\cos 2x-1}{{\left(2x\right)}^2}\times 4\times \frac{x^2}{(\cos x-1)}$

$L=\frac{1}{2}\times 4\times 2=4$

Hence, this is the answer.