Question

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

Answer 1

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

$=\underset{x\to 0}{lim}\frac{2{\sin }^{2}x}{x}$ $[\because \cos 2\theta =1-2{\sin }^2\theta ]$

$=\underset{x\to 0}{lim}2\times \frac{\sin x}{x}.\sin x=2\times 1\times 0=0$