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 Indefinite Integrals exercise 18.24 question 1 sub question (i) maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.24 question 1 sub question (i) maths textbook solution

Answers (1)

best_answer

Answer: \frac{1}{2} x+\frac{1}{2} \log |\sin x-\cos x|+c

Hint: \sin x-\cos x=t \Rightarrow(\cos x+\sin x) d x=d t

Given: \int \frac{1}{1-\operatorname{Cot} x} d x

Explanation:

\begin{aligned} &\text { Let } I=\int \frac{1}{1-\operatorname{Cot} x} \mathrm{dx} \\ &\end{aligned}

            \begin{aligned} &=\int \frac{1}{1-\frac{\cos x}{\sin x}} \mathrm{dx} \\ &=\int \frac{\sin x}{\sin x-\cos x} \mathrm{dx} \end{aligned}

            \begin{aligned} &=\frac{1}{2} \int \frac{2 \sin x}{\sin x-\cos x} \mathrm{dx} \\ &=\frac{1}{2} \int \frac{(\sin x-\cos x)+(\sin x+\cos x)}{(\sin x-\cos x)} \mathrm{dx} \end{aligned}

            =\frac{1}{2} \int 1 d x+\frac{1}{2} \int \frac{\sin x+\cos x}{\sin x-\cos x} \mathrm{dx}

\text { Let, } \quad \sin x-\cos x=t \Rightarrow(\cos x+\sin x) d x=d t

          \begin{aligned} &\mathrm{I}=\frac{x}{2}+\frac{1}{2} \int \frac{d t}{t} \\ &=\frac{x}{2}+\frac{1}{2} \log |\mathrm{t}|+\mathrm{c} \\ &=\frac{x}{2}+\frac{1}{2} \log |\operatorname{Sin} x-\operatorname{Cos} x|+c \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

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question