$\lim\limits_{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x}=$

1 2 0 none of these

1

$\lim\limits_{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x}$ $=\lim\limits_{x \rightarrow 0} \frac{\left(\cos \frac{x}{2}+\sin \frac{x}{2}\right)-\left(\sin \frac{x}{2}-\cos \frac{x}{2}\right)}{2}=\lim\limits_{x \rightarrow 0} \frac{2 \cos \frac{x}{2}}{2}=1$ Hence (1) is the correct answer.