Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that 4. sin inverse 8 / 17 + sin inverse 3 / 5 = tan inverse 77 / 36

Prove that

    4. \sin^{-1}\frac{8}{17} + \sin^{-1}\frac{3}{5} =\tan^{-1}\frac{77}{36}

Answers (1)

best_answer

Taking \sin ^{-1} \frac{8}{17} = x  

then,

\sin x = \frac{8}{17} \Rightarrow \cos x = \sqrt{1- \left ( \frac{8}{17} \right )^2} = \sqrt {\frac{225}{289}} = \frac{15}{17}.

Therefore we have-

\tan^{-1} x = \frac{8}{15} \Rightarrow x = \tan^{-1} \frac{8}{15}    

 \therefore \sin ^{-1} \frac{8}{17} = \tan ^{-1} \frac{8}{15}        .............(1).

Now, let\:\sin ^{-1} \frac{3}{5} = y,

Then,

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

So, we have now,

L.H.S.

\sin^{-1}\frac{8}{17} + \sin^{-1}\frac{3}{5}

using equations (1) and (2) we get,

 =\tan ^{-1} \frac{8}{15} + \tan^{-1} \frac{3}{4}

 =\tan^{-1} \frac{\frac{8}{15}+ \frac{3}{4}}{1-\frac{8}{15}\times \frac{3}{4}}                   [\because \tan^{-1}x + \tan^{-1}y = \tan^{-1} \frac{x+y}{1 - xy}] 

=\tan^{-1} (\frac{32+45}{60-24})

 =\tan^{-1} (\frac{77}{36}) 

=  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 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
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question