Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Write the following functions in the simplest form: 9.

Write the following functions in the simplest form:

    9. \tan^{-1} \frac{x}{\sqrt{a^2 - x^2}}, \;\; |x| < a

Answers (1)

best_answer

Given that \tan^{-1} \frac{x}{\sqrt{a^2 - x^2}}, \;\; |x| < a

Take x = a\sin \theta   or

  \theta = \sin^{-1}\left ( \frac{x}{a} \right )   and putting it in the equation above;

\tan^{-1} \frac{a\sin \theta}{\sqrt{a^2 - (a\sin \theta)^2}}

=\tan^{-1} \frac{a\sin \theta}{a\sqrt{1 - \sin^2 \theta}}

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

  =\tan^{-1}\left ( \tan \theta \right )

 =\theta = \sin^{-1}\left ( \frac{x}{a} \right )  is the simplest form.

 

Posted by

Divya Prakash Singh

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 Supplementary Exam 2025: Registrations open for Class 10, 12 private students today
anam-khan

CBSE opens application to access 10th answer scripts; verification, revaluation for Class 12 starts on May 31
anam-khan

CBSE supplementary exams 2025 from July 15; form submission starts on May 30

Latest Question