Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Solve the following equations: 13. 2tan inverse (cos x) = tan inverse (2 cosec x)

Solve the following equations:

    13. 2\tan^{-1}(\cos x) = \tan^{-1}(2\textup{cosec}x)

Answers (1)

best_answer

Given equation 2\tan^{-1}(\cos x) = \tan^{-1}(2\textup{cosec}x);

Using the formula:

\left [ 2\tan^{-1}z = \tan^{-1} \frac{2z}{1-z^2} \right ]

We can write

2\tan^{-1}(\cos x) = \tan^{-1}\left [ \frac{2\cos x}{1- (\cos x )^2 }\right ]

\tan^{-1}\left [ \frac{2\cos x}{1- (\cos x )^2 }\right ] = \tan^{-1}\left [2cosec x \right ]

So, we can equate;

=\left [ \frac{2\cos x}{1- (\cos x )^2 }\right ] = \left [2cosec x \right ]

=\left [ \frac{2\cos x}{\sin^2 x }\right ] = \left [ \frac{2}{sinx } \right ]

that implies that \cos x = \sin x.

or    \tan x =1      or    x = \frac{\pi}{4}

Hence we have solution x = \frac{\pi}{4}.

 

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

CBSE board exams 2025 from February 15; Class 10, 12 subject-wise marks distribution
anam-khan

CBSE Date Sheet 2025: Class 10, 12 board exam dates soon on cbse.gov.in; previous trends, sample papers
anam-khan

CBSE Board Exams 2025: 75% attendance must for students to be eligible, reiterates board

Latest Question