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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2012 · Mathematics · Inverse Trigonometric Functions

What is [ ^ -1 ((3)/(4))+ ^ -1 ((4)/(5))]equal to?

What is sin⁡[sin⁡−1(34)+sin⁡−1(45)]equalto?\sin \left[\sin ^{-1} \left(\frac{3}{4}\right)+\sin ^{-1}\left(\frac{4}{5}\right)\right]equal to?

Options

  1. A00
  2. B12\frac{1}{2}
  3. C11
  4. D22

Correct answer

C. 11

Step-by-step solution

\sin \left[\sin ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{4}{5}\right)\right]=\sin \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{3}{5}\right)\right]\left[\because \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}\right]=\sin \left[\frac{\pi}{2}\right]=1
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