Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain Solution R.D.Sharma Class 12 Chapter 10 Differentiation Exercise 10.3 Question 32 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 10  Differentiation  Exercise 10.3 Question 32 Maths Textbook Solution.

Answers (1)

Answer: \frac{dy}{dx}=1

Hint:

\begin{aligned} &\frac{\mathrm{d}}{\mathrm{dx}}(\text { constan } \mathrm{t})=0 ; \\ &\frac{d}{d \mathrm{x}}\left(\mathrm{x}^{\mathrm{n}}\right)=\mathrm{n} \mathrm{x}^{\mathrm{n}-1} \end{aligned}

Given:

\tan ^{-1}\left[\frac{\cos x+\sin x}{\cos x-\sin x}\right]

Solution:

\begin{aligned} &y=\tan ^{-1}\left[\frac{\cos x+\sin x}{\cos x-\sin x}\right] \\ &y=\tan ^{-1}\left[\frac{\frac{\cos x+\sin x}{\cos x}}{\frac{\cos x-\sin x}{\cos x}}\right] \\ &y=\tan ^{-1}\left[\frac{1+\tan x}{1-\tan x}\right] \\ &\text { since, } \frac{\sin x}{\cos x}=\operatorname{tian} x \end{aligned}

\begin{aligned} &y=\tan ^{-1}\left[\frac{\tan \frac{\pi}{4}+\tan x}{1-\frac{\tan \pi}{4} \tan x}\right] \\ &y=\tan ^{-1}\left[\tan \left(\frac{\pi}{4}+x\right)\right] \\ &\text { Since } \tan (A+B)=\frac{\tan A+\tan B}{1-\tan \tan B} \\ &y=\frac{\pi}{4}+x \end{aligned}                            

Differentiating it with respect to x,

\frac{dy}{dx}=0+1                                                                                        \left\{\begin{array}{l} \frac{\mathrm{d}}{\mathrm{dx}}(\text { constant })=0 \\ \frac{\mathrm{d}}{\mathrm{dx}}(\mathrm{x})=1 \end{array}\right\}

\frac{dy}{dx}=1

                                                                                                                                    

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

CBSE Class 12 supplementary admit card out; exam on July 28 for over 2.5 lakh
anam-khan

CBSE Class 12 supplementary exams 2026 datesheet out; test on July 28
anam-khan

Centre, CBSE, NCERT defend NEP three-language policy in SC; seek dismissal of pleas against framework

Latest Question