$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cot x-1}$=

Question

$(a)\;1\qquad(b)\;\large\frac{1}{2}$$\qquad(c)\;\large\frac{1}{\sqrt 2}$$\qquad(d)\;\large\frac{1}{2\sqrt 2}$