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 Trigonometric Function Exercise 3.11 Question 3 Subquestion (viii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.11 Question 3 Subquestion (viii) Maths Textbook Solution.

Answers (1)

best_answer

Answer:
x=\pm\sqrt{2}
Hint:
Here, we will use the formula
\tan^{-1}A+\tan^{-1}B=\tan^{-1}\left ( \frac{A+B}{1-AB} \right )
Given:
\tan^{-1}\left ( \frac{x-2}{x-4} \right )+\tan^{-1}\left ( \frac{x+2}{x+4} \right )=\frac{\pi }{4}
Solution:
\begin{aligned} &\tan ^{-1}\left[\frac{\left(\frac{x-2}{x-4}\right)+\left(\frac{x+2}{x+4}\right)}{1-\left(\frac{x-2}{x-4}\right)\left(\frac{x+2}{x+4}\right)}\right]=\frac{\pi}{4} \\ &\Rightarrow \tan ^{-1}\left[\frac{\frac{x-2}{x-4}+\frac{x+2}{x+4}}{1-\left(\frac{x^{2}-2^{2}}{x^{2}-4^{2}}\right)}\right]=\frac{\pi}{4} \\ &\Rightarrow \frac{x^{2}+4 x-2 x-8+x^{2}-4 x+2 x-8}{x^{2}-16-x^{2}+4}=\tan \frac{\pi}{4} \\ &\Rightarrow \frac{2 x^{2}-16}{-12}=\tan \frac{\pi}{4} \\ &\Rightarrow \frac{2 x^{2}-16}{-12}=1 \quad\left[\because \tan \frac{\pi}{4}=1\right] \end{aligned}
\! \! \! \! \! \! \! \! \! \Rightarrow 2x^{2}-16=-12\\ \Rightarrow 2x^{2}=16-12\\ \Rightarrow 2x^{2}=4\\ \Rightarrow x^{2}=2\\ \Rightarrow x=\pm \sqrt2\\

Posted by

infoexpert27

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

Board Exam Result 2025 Live: UK Board 10th, 12th results tomorrow; AP SSC, TS Inter, UP, CBSE updates
anam-khan

When will CBSE Class 12 results 2025 be declared? Last two years' trends
anam-khan

CBSE Class 10, 12 board exams 2025 from April 7 to 11 for sports students

Latest Question