JEE Math Practice Question

If the function ƒ defined on , $$\left( {{\pi \over 6},{\pi \over 3}} \right)$$ by $$$f(x) = \left\{ {\begin{matrix} {{{\sqrt 2 {\mathop{\rm cosx}\nolimits} - 1} \over {\cot x - 1}},} & {x \ne {\pi \over 4}} \\ {k,} & {x = {\pi \over 4}} \\ \end{matrix} } \right.$$$ is continuous, then k is equal to

1. A.1
2. B.1 / $$\sqrt 2$$
3. C.$${1 \over 2}$$
4. D.2