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 4 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.11 Question 4 Maths Textbook Solution.

Answers (1)

Answer:
\tan^{-1}2^{n}-\frac{\pi }{4}
Hint:
We have to focus on calculation of infinite series.
Given:\begin{aligned} &\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{2}{9}\right)+\ldots+\left.\tan ^{-1}\left(\frac{2^{n-1}}{1+2^{2 n-1}}\right)\right|_{-1} \\ \end{aligned}

Solution:
\begin{aligned} &\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{2}{9}\right)+\ldots+\left.\tan ^{-1}\left(\frac{2^{n-1}}{1+2^{2 n-1}}\right)\right|_{-1} \\ &=\tan ^{-1}\left(\frac{2-1}{1+2 x 1}\right)+\tan ^{-1}\left(\frac{4-2}{1+4 x 2}\right)+\ldots+\tan ^{-1}\left(\frac{2^{n}-2^{n-1}}{1+2^{n} \cdot 2^{n-1}}\right) \\ &=\left(\tan ^{-1} 2-\tan ^{-1} 1\right)+\left(\tan ^{-1} 4-\tan ^{-1} 2\right)+\ldots .+\left(\tan ^{-1} 2^{n}-\tan ^{-1} 2^{n-1}\right) \\ &=\tan ^{-1} 2^{n}-\tan ^{-1} 1 \\ &=\tan ^{-1} 2^{n}-\frac{\pi}{4} \end{aligned}

 

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 Date Sheet 2025: CBSE, UPMSP, MPBSE, Class 10, 12 board exam dates out; BSEB, CGBSE schedules soon
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

Latest Question