# Lim X → π 2 Cot X π 2 − X - Mathematics

$\lim_{x \to \frac{\pi}{2}} \frac{\cot x}{\frac{\pi}{2} - x}$

#### Solution

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.8 | Q 9 | Page 62