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Prove that : \[ sin^{-1}\frac{3}{5}+sin^{-1}\frac{8}{17}=cos^{-1}\frac{36}{85} \]

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Toolbox:
  • \( sin^{-1}x+sin^{-1}y=sin^{-1} \bigg[ x\sqrt {1-y^2}+y\sqrt{1-x^2} \bigg]\)
  • \( sin^{-1}x=cos^{-1} \sqrt{1-x^2}\)
L.H.S
\( sin^{-1} \bigg[ \large\frac{3}{5} \sqrt{1-\large\frac{69}{289}}+\large\frac{8}{17} \sqrt{1-\large\frac{9}{25}} \bigg]\)
\( = sin^{-1} \bigg[ \large\frac{77}{85} \bigg]\)
\( = cos^{-1} \large\frac{36}{85}\)

 

answered Mar 1, 2013 by thanvigandhi_1
edited Mar 19, 2013 by thanvigandhi_1
 

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