$\lim\limits_{x\to 1}\large\frac{\sqrt{1-\cos 2(x-1)}}{x-1}$=

Question

$\begin{array}{1 1}(a)\;\text{exists and it equals } \sqrt 2 \\(b)\;2\text{exists and it equals } -\sqrt 2\\(c)\;\text{does not exists because }x-1\to 0\\(d)\;\text{does not exists because } LHL\neq RHL\end{array}$