Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12  chapter Inverse Trigonometric Functions exercise 3.5 question 1 sub question (iv) maths

Explain solution RD Sharma class 12  chapter Inverse Trigonometric Functions exercise 3.5 question 1 sub question (iv) maths
 

Answers (1)

\frac{-\pi}{2}      

Hints: \operatorname{cosec}^{-1} is a function whose range of principal branch is \left [ \frac{-\pi}{2}, \frac{\pi}{2} \right ] \left \{ 0 \right \}

Thus, \operatorname{cosec}^{-1} : R-(-1,1)→\left [ \frac{-\pi}{2}, \frac{\pi}{2} \right ] \left \{ 0 \right \}

Given: \operatorname{cosec}^{-1}\left(2 \cos \frac{2 \pi}{3}\right)

Explanation: let y = \left(2 \cos \frac{2 \pi}{3}\right)

\operatorname{cosec}y = \left(2 \cos \frac{2 \pi}{3}\right)

Range of function \operatorname{cosec}^{-1} is \left [ \frac{-\pi}{2}, \frac{\pi}{2} \right ] \left \{ 0 \right \}

Thus, \operatorname{cosec}y = \left(2 \cos \frac{2 \pi}{3}\right)

\operatorname{cosec}y = 2 \times \frac{-1}{2}                                                                                                                       \left [\cos \frac{2\pi }{3}= \frac{-1}{2} \right ]

\operatorname{cosec}y =-1

\begin{aligned} &\operatorname{cosec} y=\operatorname{cosec}\left(\frac{-\pi}{2}\right)\\ &y=\frac{-\pi}{2} \in\left[\frac{-\pi}{2}, \frac{\pi}{2}\right], y \neq 0\\ &\text { Hence principal value of } \operatorname{cosec}^{-1}\left(2 \cos \frac{2 \pi}{3}\right) \text { is } \frac{-\pi}{2} \end{aligned}

Posted by

infoexpert24

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