If $f\left(x\right)=\frac{\sqrt{1+2\sin x}-\sqrt{1-2\sin x}}{x}$ is continuous on $R,$ then $f\left(0\right)=$

$$\begin{gathered} f\left(0\right)=\underset{x\to 0}{Lt}f\left(x\right) \\ =\underset{x\to 0}{Lt}\frac{\sqrt{1+2\sin x}-\sqrt{1-2\sin x}}{x} \\ =\underset{x\to 0}{Lt}\frac{(1+2\sin x)-(1-2\sin x)}{\sqrt{1+2\sin x}+\sqrt{1-2\sin x}}.\frac{1}{x} \end{gathered}$$ on rationalisation

$=\underset{x\to 0}{Lt}\frac{4\sin x}{x\left[\sqrt{1+2\sin x}+\sqrt{1-2\sin x}\right]}=2$