Q182 / 270 · NDA 2012 (Phase 2) · Mathematics

What is $\sin \left[\sin ^{-1}\left(\frac{3}{4}\right)+\sin ^{-1}\left(\frac{4}{5}\right)\right]$ equal to?

  • A
    $0$
  • B
    $\frac{1}{2}$
  • Correct answer
    C
    $1$
  • D
    $2$

Solution

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

Hence, the correct answer is option: 'C'.

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