Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Choose the correct answers in Exercises 41 to 44. Integral cos 3x by (sin x Plus cos x) to the power 2 dx is equal to

Choose the correct answers in Exercises 41 to 44.

    Q42.    \int\frac{\cos 2x}{(\sin x + \cos x)^2}dx is equal to

                (A)    \frac{-1}{\sin x + \cos x} + C

                (B)    \log |{\sin x + \cos x} |+ C

                (C)    \log |{\sin x- \cos x} |+ C

                (D)    \frac{1}{(\sin x + \cos x)^2} + C

Answers (1)

best_answer

\\\frac{\cos 2x}{(\sin x + \cos x)^2}\\ =\frac{cos^{2}x-sin^{2}x}{(\sin x + \cos x)^2}\\ =\frac{(\sin x + \cos x)(\cos x-\sin x)}{(\sin x + \cos x)^2} \\=\frac{(\cos x-\sin x)}{(\sin x + \cos x)}                     cos2x=cos2x-sin2x

let sinx+cosx=t,(cosx-sinx)dx=dt

hence the given integral can be written as

\\\int\frac{\cos 2x}{(\sin x + \cos x)^2}dx\\ =\int \frac{dt}{t}\\ =log|t|+c \\=log|cosx+sinx|+c

B is correct

Posted by

Sayak

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 Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question