Evaluate `lim_(xto (pi^(-))/(2)) (cosx)^(cosx).`

Explanation

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

### Step 1: Substitute and Simplify
As \( x \) approaches \( \frac{\pi}{2} \) from the left, \( \cos x \) approaches \( 0 \). Therefore, we can let \( y = \cos x \). As \( x \to \frac{\pi}{2}^- \), \( y \to 0^+ \). We need to evaluate the limit:
\[ \lim_{y \to 0^+} y^y \]

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