Question

The value of $\underset{x\to 0}{lim}\frac{\cos 2x-1}{\cos x-1}$ is

• A. $0$
• B. $1$
• C. $4$
• D. $\infty$

Answer 1

The correct option is C $4$

$\underset{x\to 0}{lim}\frac{\cos 2x-1}{\cos x-1}$
$\underset{x\to 0}{lim}\frac{2{\cos }^{2}x-1-1}{\cos x-1}$
$\underset{x\to 0}{lim}\frac{2(\cos x-1)(\cos x+1)}{\cos x-1}$
$\underset{x\to 0}{lim}2(\cos x+1)=2(1+1)=4$