`lim_(x-pi/2) (cot x - cosx)/(pi-2x)^3` equals: (1) `1/8` (2) `1/4` (3) `1/24` (4) `1/16`

Explanation

To solve the limit problem \( \lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2x)^3} \), we can follow these steps:

### Step 1: Substitute \( x = \frac{\pi}{2} + h \)
We start by substituting \( x \) with \( \frac{\pi}{2} + h \), where \( h \to 0 \) as \( x \to \frac{\pi}{2} \).

\[ \lim_{h \to 0} \frac{\cot\left(\frac{\pi}{2} + h\right) - \cos\left(\frac{\pi}{2} + h\right)}{\left(\pi - 2\left(\frac{\pi}{2} + h\right)\right)^3} \]
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