Question

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

Answer 1

$\underset{xx\to 0}{lim}\frac{\cos 2x-1}{\cos x-1}\left(0÷0from\right)$

using L' hosptital rule

$\underset{x\to 0}{lim}\frac{-2\sin 2x}{-\sin x}\left(0÷0from\right)$

again using L' hospital rule

$\underset{x\to 0}{lim}\frac{2\cos 2x}{\cos x}=2$