Evaluate: `(lim)_(x->pi/2)(pi/2-x)t a n x`

Explanation

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

### Step 1: Rewrite the tangent function
We know that \( \tan x = \frac{1}{\cot x} \). Therefore, we can rewrite the limit as:
\[ L = \lim_{x \to \frac{\pi}{2}} \left( \frac{\pi}{2} - x \right) \frac{1}{\cot x} \]

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