Evaluate: `(lim)_(x->pi/2)(cot x)/(pi/2-x)`

Explanation

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

### Step 1: Identify the form of the limit
First, we substitute \( x = \frac{\pi}{2} \) into the expression:
\[ \cot\left(\frac{\pi}{2}\right) = 0 \quad \text{and} \quad \frac{\pi}{2} - \frac{\pi}{2} = 0 \]
Thus, we have the indeterminate form \( \frac{0}{0} \).
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