Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 5 sub question (iii) maths textbook solution

Please solve RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 5 sub question (iii) maths textbook solution

Answers (1)

Answer:    -\frac{\pi }{5}

Hint: The range of principal value of    \operatorname{cosec}^{-1} \text { is }\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}
Given:    \operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{6 \pi}{5}\right)

Explanation:

First we solve \operatorname{cosec}\left(\frac{6 \pi}{5}\right)

            \operatorname{cosec}\left(\frac{6 \pi}{5}\right)=\operatorname{cosec}\left(\pi+\frac{\pi}{5}\right)

As we know,  \operatorname{cosec}(\pi+\theta)=-\operatorname{cosec} \theta

Then,     \operatorname{cosec}\left(\pi+\frac{\pi}{5}\right)=-\operatorname{cosec}\left(\frac{\pi}{5}\right)

            -\operatorname{cosec}\left(\frac{\pi}{5}\right)=\operatorname{cosec}\left(-\frac{\pi}{5}\right)

As         \operatorname{cosec}(-x)=-\operatorname{cosec} x

By substituting this value in \operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{6 \pi}{5}\right) we get,

             \operatorname{cosec}^{-1}\left(\operatorname{cosec}\left(-\frac{\pi}{5}\right)\right)

As we know,   \operatorname{cosec}^{-1}(\operatorname{cosec} x)=x \text { when } x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}

            \operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{6 \pi}{5}\right)=-\frac{\pi}{5}

Posted by

infoexpert26

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