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 RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.23 Question 14 Maths Textbook Solution.

Need Solution For  RD Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise 18.23 Question 14 Maths Textbook Solution.

Answers (1)

Answer : =-\frac{1}{2} \log \left|\operatorname{cosec}\left(x-\frac{\pi}{3}\right)+\cot \left(x-\frac{\pi}{3}\right)\right|+c

Hint : To solve this question we have to use formula of \sin \left(x-\frac{\pi}{3}\right)

Given : \int \frac{1}{\sin x-\sqrt{3} \cos x} d x

Solution : \int \frac{1}{\sin x-\sqrt{3} \cos x} dx

\begin{aligned} &=\int \frac{1}{2\left(\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x\right)} d x \\ &=\frac{1}{2} \int \frac{1}{\sin x \cos \frac{\pi}{3}-\cos x \sin \frac{\pi}{3}} d x \end{aligned}

\begin{aligned} &=\frac{1}{2} \int \frac{1}{\sin \left(x-\frac{\pi}{3}\right)} d x \\ &=\frac{1}{2} \int \operatorname{cosec}\left(x-\frac{\pi}{3}\right) d x \\ &t=\left(x-\frac{\pi}{3}\right) \end{aligned}

\begin{aligned} &\frac{d t}{d x}=1 \\ &d t=d x \\ &=-\frac{1}{2} \log |\cos e c t+\cos t|+c \\ &=-\frac{1}{2} \log \left|\cos e c\left(x-\frac{\pi}{3}\right)+\cot \left(x-\frac{\pi}{3}\right)\right|+c \end{aligned}

Note: Final answer is not matching with the book.

 

Posted by

infoexpert23

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

Latest Question