^ -1 (3 5 )+ ^ -1 (8 17 )= - Vidyadip

MCQ

$\sin ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{8}{17}\right)=$

A
$\sin ^{-1}\left(\frac{57}{85}\right)$
B
$\sin ^{-1}\left(\frac{47}{87}\right)$
C
$\sin ^{-1}\left(\frac{67}{85}\right)$
✓
$\sin ^{-1}\left(\frac{77}{85}\right)$

✓

Answer

Correct option: D.

$\sin ^{-1}\left(\frac{77}{85}\right)$

(D) $\sin ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{8}{17}\right)$
$=\sin ^{-1}\left(\frac{3}{5} \sqrt{1-\left(\frac{8}{17}\right)^2}+\frac{8}{17} \sqrt{1-\left(\frac{3}{5}\right)^2}\right)$
$\ldots\left[\because \sin ^{-1} x+\sin ^{-1} y=\sin ^{-1} x \sqrt{1-y^2}+y \sqrt{1-x^2}\right]$
$=\sin ^{-1}\left(\frac{3}{5} \times \frac{15}{17}+\frac{8}{17} \times \frac{4}{5}\right)=\sin ^{-1}\left(\frac{77}{85}\right)$

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