Find `lim_(x rarr pi){sin(x- pi)}/{(pi(pi-x)}`

Explanation

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

### Step 1: Substitute \( z = x - \pi \)
We start by substituting \( z = x - \pi \). As \( x \) approaches \( \pi \), \( z \) approaches \( 0 \). Thus, we can rewrite the limit in terms of \( z \):

\[ x = z + \pi \implies \pi - x = \pi - (z + \pi) = -z \]
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