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Prove that : $\sin^{-1}\frac{3}{5} + \sin^{-1}\frac{8}{17}=\sin^{-1}\frac{77}{85} $

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Toolbox:
  • \( sin^{-1}x+sin^{-1}y\)
  • \(= sin^{-1} \bigg[ x\sqrt{1-y^2}+y\sqrt{1-x^2} \bigg]\)
L.H.S \( sin^{-1} \bigg[ \frac{3}{5} \sqrt{1-\frac{64}{289}}+\frac{8}{17} \sqrt{1-\frac{9}{25}} \bigg] \)
\( = sin^{-1} \bigg[ \frac{77}{85} \bigg] = R.H.S \)
answered Mar 1, 2013 by thanvigandhi_1
 

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