Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Evaluate the following limits limit x tends to 0 cosec x - cot x

21.   Evaluate the following limits \lim_{x \rightarrow 0} \left ( \csc x - \cot x \right )

Answers (1)

best_answer

\lim_{x \rightarrow 0} \left ( \csc x - \cot x \right )

On putting the limit directly the function takes infinity by infinity form, So we simplify the function and then put the limit

\lim_{x \rightarrow 0} \left ( \csc x - \cot x \right )

=\lim_{x \rightarrow 0} \left (\frac{1}{sinx}-\frac{cosx}{sinx}\right )

=\lim_{x \rightarrow 0} \left (\frac{1-cosx}{sinx}\right )

=\lim_{x \rightarrow 0} \left (\frac{2sin^2(\frac{x}{2})}{sinx}\right )

=\lim_{x \rightarrow 0} \left (\frac{2sin^2(\frac{x}{2})}{(\frac{x}{2})^2}\right )\left ( \frac{(\frac{x}{2})^2}{sinx} \right )

=\lim_{x \rightarrow 0} \frac{2}{4}\left (\frac{sin^2(\frac{x}{2})}{(\frac{x}{2})^2}\right )\left ( \frac{(x)}{sinx} \right )\cdot x

=\frac{2}{4}\times (1)^2\times0

=0   (Answer)

 

Posted by

Pankaj Sanodiya

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question