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If the function $f$ defined on $\left(\dfrac{\pi}{6}, \dfrac{\pi}{3}\right)$ by
$$f(x) = \begin{cases} \dfrac{\sqrt{2}\cos x - 1}{\cot x - 1}, & x \neq \dfrac{\pi}{4} \ k, & x = \dfrac{\pi}{4} \end{cases}$$
is continuous, then $k$ is equal to:
(1) $2$
(2) $\dfrac{1}{2}$
(3) $1$
(4) $\dfrac{1}{\sqrt{2}}$
BETA
