Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 10

Provide solution for RD Sharma math class 12 chapter 3 Inverse Trigonometric Functions exercise Very short answer question 10

Answers (1)

Answer: \frac{1}{\sqrt{x^{2}+1}}                                             

Given: \sin \left(\cot ^{-1} x\right)

Hint: \sin \left(\cot ^{-1} x\right)=\sin \left(\tan ^{-1} \frac{1}{x}\right)\\\\

\tan ^{-1} x=\sin \left(\frac{x}{\sqrt{1+x^{2}}}\right)

Solution:

        \cot ^{-1} x=\tan ^{-1} \frac{1}{x}

      \sin \left(\cot ^{-1} x\right) =\sin \left(\tan ^{-1} \frac{1}{x}\right) \\

                                =\sin \left[\sin ^{-1}\left(\frac{\frac{1}{x}}{\sqrt{x^{2}+\frac{1}{x}}}\right)\right] \\

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

                               =\frac{1}{\sqrt{x^{2}+1}} \quad \therefore\left(\sin \left(\sin ^{-1} x\right)=x\right)

 

Posted by

infoexpert22

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