Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that 3. 2 sin inverse 3 / 5 = tan inverse 24 / 7

Prove that

    3. 2\sin^{-1}\frac{3}{5} = \tan^{-1}\frac{24}{7}

Answers (1)

best_answer

To prove: 2\sin^{-1}\frac{3}{5} = \tan^{-1}\frac{24}{7};

L.H.S=2\sin^{-1}\frac{3}{5}

Assume that  \sin^{-1}\frac{3}{5} = x 

then we have \sin x = \frac{3}{5}.

or \cos x = \sqrt{1-\left (\frac{3}{5} \right )^2} = \frac{4}{5}

Therefore we have

 \tan x = \frac{3}{4}\:\:or\:\:x = \sin^{-1} \frac{3}{5} = \tan^{-1} \frac{3}{4}

Now,

We can write L.H.S as

 2\sin^{-1}\frac{3}{5} = 2\tan^{-1}\frac{3}{4}

 =\tan^{-1} \left [\frac{2\times\frac{3}{4}}{1- \left ( \frac{3}{4} \right )^2} \right ]    as we know    \left [2\tan^{-1} x = \tan^{-1} \frac{2x}{1-x^2} \right ]

 =\tan^{-1} \left [\frac{\frac{3}{2}}{\left ( \frac{16-9}{16} \right )} \right ] = \tan^{-1}\left ( \frac{3}{2}\times \frac{16}{7} \right )

 =\tan^{-1} \frac{24}{7}=R.H.S  

L.H.S = R.H.S

 

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 board exams 2025 from February 15; Class 10, 12 subject-wise marks distribution
anam-khan

CBSE Date Sheet 2025: Class 10, 12 board exam dates soon on cbse.gov.in; previous trends, sample papers
anam-khan

CBSE Board Exams 2025: 75% attendance must for students to be eligible, reiterates board

Latest Question