\[\lim_{x \to \frac{\pi}{4}} \frac{{cosec}^2 x - 2}{\cot x - 1}\]

\[\lim_{x \to \frac{\pi}{4}} \left[ \frac{{cosec}^2 x - 2}{\cot x - 1} \right]\]\[ = \lim_{x \to \frac{\pi}{4}} \left[ \frac{1 + \cot^2 x - 2}{\cot x - 1} \right]\]\[ = \lim_{x \to \frac{\pi}{4}} \left[ \frac{\cot^2 x - 1}{\cot x - 1} \right]\]\[ = \lim_{x \to \frac{\pi}{4}} \left[ \frac{\left( \cot x - 1 \right) \left( \cot x + 1 \right)}{\left( \cot x - 1 \right)} \right]\]\[ = \cot \frac{\pi}{4} + 1\]\[ = 2\]

Lim X → π 4 C O S E C 2 X − 2 Cot X − 1 - Mathematics

प्रश्न

$lim_{x \to \frac{π}{4}} \frac{{c o s e c}^{2} x - 2}{\cot x - 1}$

उत्तर

$lim_{x \to \frac{π}{4}} [\frac{{c o s e c}^{2} x - 2}{\cot x - 1}]$
$= lim_{x \to \frac{π}{4}} [\frac{1 + \cot^{2} x - 2}{\cot x - 1}]$
$= lim_{x \to \frac{π}{4}} [\frac{\cot^{2} x - 1}{\cot x - 1}]$
$= lim_{x \to \frac{π}{4}} [\frac{(\cot x - 1) (\cot x + 1)}{(\cot x - 1)}]$
$= \cot \frac{π}{4} + 1$
$= 2$

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Concept of Limits - Algebra of Limits

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Q 2 Q 1 Q 3

पाठ 29: Limits - Exercise 29.9 [पृष्ठ ६५]

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आरडी शर्मा Mathematics [English] Class 11

पाठ 29 Limits
Exercise 29.9 | Q 2 | पृष्ठ ६५

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Concept of Limits - Algebra of Limits

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Lim X → π 4 C O S E C 2 X − 2 Cot X − 1 - Mathematics

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