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 Inverse Trignometric Functions exercise 3.7 question 7 sub question (i) maths textbook solution

Please solve RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 7 sub question (i) maths textbook solution

Answers (1)

Answer:  \sec ^{-1} \frac{x}{a}

Hint: The range of principal value of   \cot ^{-1} \text { is }[0, \pi]
Given:  \cot ^{-1}\left\{\frac{a}{\sqrt{x^{2}-a^{2}}}\right\},|x|>a

Explanation:

Let x=a \sec \theta

Now, we put value of  x  in given question.

            \begin{aligned} &\cot ^{-1}\left\{\frac{a}{\sqrt{(a \sec \theta)^{2}-a^{2}}}\right\} \\ &\cot ^{-1}\left\{\frac{a}{\sqrt{a^{2} \sec ^{2} \theta-a^{2}}}\right\} \\ &\cot ^{-1}\left\{\frac{a}{\sqrt{a^{2}\left(\sec ^{2} \theta-1\right)}}\right\} \end{aligned}

As we know   1+\tan ^{2} \theta=\sec ^{2} \theta

            \begin{aligned} &\sec ^{2} \theta-1=\tan ^{2} \theta \\ &\cot ^{-1}\left\{\frac{a}{\sqrt{a^{2} \tan ^{2} \theta}}\right\} \end{aligned}

Now we remove square root

            \begin{aligned} &\cot ^{-1}\left\{\frac{a}{a \tan \theta}\right\} \\ &\cot ^{-1}\left\{\frac{1}{\tan \theta}\right\} \end{aligned}

As we know,   \cot \theta=\frac{1}{\tan \theta}

            \cot ^{-1}(\cot \theta)=\theta

As we know,   \cot ^{-1}(\cot \theta), \theta \in[0, \pi]

            \begin{aligned} &x=a \sec \theta \\ &\theta=\sec ^{-1} \frac{x}{a} \end{aligned}

Hence, \cot ^{-1}\left\{\frac{a}{\sqrt{x^{2}-a^{2}}}\right\},|x|>a \text { is } \sec ^{-1} \frac{x}{a}

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 Exam Date Sheet 2025: CBSE, UPMSP, MPBSE, Class 10, 12 board exam dates out; BSEB, CGBSE schedules soon
anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4

Latest Question