Evaluate the following limit: `lim_(x->pi/2)((pi/2-x)sin x-2cos x)/((pi/2-x)+cot x)`

Explanation

To evaluate the limit

\[ L = \lim_{x \to \frac{\pi}{2}} \frac{\left(\frac{\pi}{2} - x\right) \sin x - 2 \cos x}{\left(\frac{\pi}{2} - x\right) + \cot x} \]

we start by substituting \(x = \frac{\pi}{2}\):

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