If `f(x)=(sqrt(2)cosx-1)/(cotx-1),x!=pi/4dot` Find the value of `f(pi/4)` so that `f(x)` becomes continuous at `x=pi/4dot`

Explanation

To find the value of \( f\left(\frac{\pi}{4}\right) \) such that \( f(x) \) becomes continuous at \( x = \frac{\pi}{4} \), we need to evaluate the limit of \( f(x) \) as \( x \) approaches \( \frac{\pi}{4} \).

Given:
\[ f(x) = \frac{\sqrt{2} \cos x - 1}{\cot x - 1} \]

### Step 1: Evaluate \( f\left(\frac{\pi}{4}\right) \)
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