limx→π/2 acot⁡x−acos⁡xcot⁡x−cos⁡x,a>0 is equal to

A
$\log_{e} (\frac{π}{2})$
B
$\log_{e} 2$
C
$\log_{e} a$
D
$a$

Solution:

We have,

$\begin{array}{l} = lim_{=\to - / 2} \frac{a^{\cot x} - a^{\cos x}}{\cot x - \cos x} \\ = lim_{=\to π / 2} a^{\cos x} (\frac{a^{\cot x - \cos x} - 1}{\cot x - \cos x}) = a^{\cos π / 2} \times \log_{e} a = \log_{e} a \end{array}$

Related content

Test your English Vocabulary

CUET Exam Dates 2024 – Application Form, Fees, Eligibility

CBSE Class 12 IP Answer Key 2024,Informatics Practices Paper Solution For SET 1, 2, 3, 4

CUET UG Cut Off 2024, Category, Universities and Colleges Wise Expected Cut Off

Modal Verbs

Helping Verbs

Letter To Your Friend About Your School Trip

Action Verbs

CUET 2024 – List of Colleges and Participating Universities Accepting CUET Exam Score

SRMJEEE Online Test Series – Practice Papers