Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 32 maths

Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 32 maths

Answers (1)

Answer:

        1

Hint:

        Differentiate the function w.r.t x

Given:

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

Solution: 

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

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

\frac{d y}{d x}=\frac{(\cos x-\sin x)^{2}}{(\cos x-\sin x)^{2}+(\sin x+\cos x)^{2}} \times  \left[\frac{(\cos x-\sin x) \frac{d}{d x}(\sin x+\cos x)-(\sin x+\cos x) \frac{d}{d x}(\cos x-\sin x)}{(\cos x-\sin x)^{2}}\right]

        =\frac{(\cos x-\sin x)^{2}}{(\cos x-\sin x)^{2}+(\sin x+\cos x)^{2}}\left[\frac{(\cos x-\sin x)(\cos x-\sin x)-(\sin x+\cos x)(-\sin x-\cos x)}{(\cos x-\sin x)^{2}}\right]

       =\frac{(\cos x-\sin x)^{2}}{(\cos x-\sin x)^{2}+(\sin x+\cos x)^{2}}\left[\frac{(\cos x-\sin x)(\cos x-\sin x)+(\sin x+\cos x)(\sin x+\cos x)}{(\cos x-\sin x)^{2}}\right]

      \begin{aligned} &=\frac{(\cos x-\sin x)^{2}}{(\cos x-\sin x)^{2}(\sin x+\cos x)^{2}} \times \frac{(\cos x-\sin x)^{2}+(\sin x+\cos x)^{2}}{(\cos x-\sin x)^{2}} \\ &\frac{d y}{d x}=1 \end{aligned}

    

 

 

 

Posted by

infoexpert26

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 Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO
anam-khan

Board Exam Date 2025 Live: CBSE, ICSE, BSEB, MPBSE Class 10, 12 timetable out; Punjab, Rajasthan schedule soon
anam-khan

CBSE Board Exams 2025: Guidelines issued for Class 10, 12 practicals

Latest Question