Solve this following

Question:

If the function $f$ defined on $\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ by

$f(x)=\left\{\begin{array}{cc}\frac{\sqrt{2} \cos x-1}{\cot x-1}, & x \neq \frac{\pi}{4} \\ \mathrm{k}, & \mathrm{x}=\frac{\pi}{4}\end{array}\right.$

then $\mathrm{k}$ is equal to

 

  1. $\frac{1}{2}$

  2. 1

  3. $\frac{1}{\sqrt{2}}$

  4. 2


Correct Option: 1,

Solution:

 

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