Explanation

(b)
$\lim_{x \rightarrow \frac{\pi}{2}}\frac{\cot{x - \cos x}}{(\pi - 2x)^{3}}$
$= \ \lim_{h \rightarrow 0}\frac{\cot{\left( \frac{\pi}{2} + h \right) - \cos\left( \frac{\pi}{2} + h \right)}}{( - 2h)^{3}}$
$= \lim_{h \rightarrow 0}\frac{- \tan{h + \sin h}}{( - 2h)^{3}}$
$= \lim_{h \rightarrow 0}\ \frac{\sin{h(1 - \cos h)}\ }{\cos{h \times 8h^{3}}}$
$= \frac{1}{8}\lim_{h \rightarrow 0}\ \frac{\sin h}{h} \times \frac{2\sin^{2}{h/2}}{4(h/2)^{2}} \times \frac{1}{\cos h} = \frac{1}{16}$