Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 9 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 9 Maths Textbook Solution.

Answers (1)

Answer:

\sin 2 x+\tan x-2 x+c

Given:

\int \sec ^{2} x \cos ^{2} 2 x d x

Hint:

Use trigonometry identity.

Solution:   

\int \sec ^{2} x \cos ^{2}(2 x) d x

    =\int \sec ^{2} x\left(2 \cos ^{2} x-1\right)^{2} d x \quad\left[\because \cos 2 x=2 \cos ^{2} x-1\right]

     =\int \sec ^{2} x\left(4 \cos ^{4} x-4 \cos ^{2} x+1\right) d x

  =\int 4 \cos ^{2} x-4+\sec ^{2} x d x \quad\left[\because \frac{1}{\sec ^{2} x}=\cos ^{2} x\right]

 =4 \int \cos ^{2} x-1 d x+\int \sec ^{2} x d x

=2 \int 2 \cos ^{2} x d x-4 \int d x+\int \sec ^{2} x d x

=2 \int(1+\cos 2 \mathrm{x}) \mathrm{dx}-4 \int \mathrm{dx}+\int \sec ^{2} \mathrm{x} \mathrm{dx}

=2 x+2 \frac{\sin 2 x}{2}-4 x+\tan x+c

=\sin 2 x-2 x+\tan x+c

 

Posted by

infoexpert21

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 Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question