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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives2 Marks
Question
Evaluate $\mathop {\lim }\limits_{x \to 0} ({\text{cosec }}x - \cot x)$
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Answer

Here $\mathop {\lim }\limits_{x \to 0} ({\text{cosec }}x - \cot x)$
$= \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{\sin x}} - \frac{{\cos x}}{{\sin x}}} \right)$
$= \mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos x}}{{\sin x}}$
$ = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\sin }^2}x/2}}{{2\sin x/2\cos x/2}} = \mathop {\lim }\limits_{x \to 0} \tan x/2 = 0$

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