Evaluate the following limit: `lim_(x->pi/4)(2-cos e c^2x)/(1-cot x)`

Explanation

To evaluate the limit \( \lim_{x \to \frac{\pi}{4}} \frac{2 - \cos^2 x}{1 - \cot x} \), we can follow these steps:

### Step 1: Substitute the limit
First, we substitute \( x = \frac{\pi}{4} \) into the expression to check if it leads to an indeterminate form.

\[ \cot\left(\frac{\pi}{4}\right) = 1 \quad \text{and} \quad \cos^2\left(\frac{\pi}{4}\right) = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2} \]
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