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 3 Inverse Trigonometric Functions exercise Very short answer question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 5 maths textbook solution

Answers (1)

Answer: -2 \tan ^{-1} x

Given:

x<0, \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)

Hint:

\frac{1-\tan ^{2} x}{1+\tan ^{2} x}=\cos 2 x

Solution:

Let, x=\tan y\\\\

\begin{aligned} \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) &=\cos ^{-1}\left(\frac{1-\tan ^{2} y}{1+\tan ^{2} y}\right) \\ &=\cos ^{-1}(\cos 2 y) \\ &=2 y-(1) \end{aligned}

The value of x  is negative, so let x=-a  where a>0 .           

\begin{array}{l} -a=\tan y \\\\ y=\tan ^{-1}(-a) \end{array}

 

Now,

\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)=2 y          Using (1)

\begin{array}{l} =2 \tan ^{-1}(-a) \\\\ =2 \tan ^{1} x \quad[\therefore x=-a] \end{array}

Posted by

infoexpert22

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: Guidelines issued for Class 10, 12 practicals
anam-khan

Board Exam Date Sheet 2025 Live: ICSE, ISC, CBSE, MP time table out; BSEB routine soon
anam-khan

Board exam dates 2025: CBSE, CISCE, UP, MP, Maharashtra, TN time table out; state-wise updates

Latest Question