Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the value of the following: 2. tan inverse (tan 7 pi over 6)

Find the value of the following:

    2. \tan^{-1}\left(\tan\frac{7\pi}{6} \right )

Answers (1)

best_answer

We have given \tan^{-1}\left(\tan\frac{7\pi}{6} \right );

so, as we know  \tan^{-1}\left(\tan x \right ) =x \:\:if\:\:x\epsilon \left ( -\frac{\pi}{2}, \frac{\pi}{2} \right )

So, here we have \frac{7\pi}{6} \notin \left ( -\frac{\pi}{2}, \frac{\pi}{2} \right ).

Therefore we can write \tan^{-1}\left(\tan\frac{7\pi}{6} \right ) as:

=\tan^{-1}\left(\tan \left (2\pi - \frac{5\pi}{6} \right ) \right )           \left [ \because \tan(2\pi - x) = -\tan x \right ]

=\tan^{-1}\left[-\tan \left ( \frac{5\pi}{6} \right ) \right ]

=\tan^{-1}\left[\tan \left (\pi- \frac{5\pi}{6} \right ) \right ]

=\tan^{-1}\left[\tan \left (\frac{\pi}{6} \right ) \right ]\:\:where\:\:\frac{\pi}{6} \epsilon \left ( -\frac{\pi}{2}, \frac{\pi}{2} \right ) 

\therefore \tan^{-1} \left ( \tan \frac{7\pi}{6} \right ) = \tan^{-1} \left ( \tan \frac{\pi}{6} \right ) = \frac{\pi}{6}.

 

Posted by

Divya Prakash Singh

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

Iran-Israel War: CBSE cancels Class 10th, postpones 12th exams in middle east countries
anam-khan

CBSE Class 12 Psychology Analysis: Paper ‘easy, well-balanced’; case-based, mix of theory, application
anam-khan

CBSE Board Exam 2026 March 5 LIVE: Class 12 Psychology question paper analysis; answer key, updates

Latest Question