Answer 1

\[\lim_{x \to \frac{\pi}{2}} \frac{\cot x}{\frac{\pi}{2} - x}\]
\[ = \lim_{h \to 0} \frac{\cot \left( \frac{\pi}{2} - h \right)}{\frac{\pi}{2} - \left( \frac{\pi}{2} - h \right)}\]
\[ \Rightarrow \lim_{x \to 0} \frac{\tan h}{h} = 1\]