`(lim)_(x->pi/2)(tan2x)/(x-pi/2)`

Explanation

To solve the limit \(\lim_{x \to \frac{\pi}{2}} \frac{\tan(2x)}{x - \frac{\pi}{2}}\), we can follow these steps:

### Step 1: Substitute \(y = x - \frac{\pi}{2}\)
Let \(y = x - \frac{\pi}{2}\). Then, as \(x\) approaches \(\frac{\pi}{2}\), \(y\) approaches \(0\). We can express \(x\) in terms of \(y\):
\[ x = \frac{\pi}{2} + y \]

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