Question

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

Answer 1

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

${lim}_{x\to 0}\frac{\sqrt{\frac{2{\sin }^{2}x}{2}}}{x}$ as ${\cos }^{2}x=1-2{\sin }^{2}x$

$\Rightarrow {lim}_{x\to 0}\frac{\sin x}{x}=1$