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Show that sin^(-1)(3/5)-sin^(-1)(8/17)=c...

Show that `sin^(-1)(3/5)-sin^(-1)(8/17)=cos^(-1)(84/85)`

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To show that \( \sin^{-1}\left(\frac{3}{5}\right) - \sin^{-1}\left(\frac{8}{17}\right) = \cos^{-1}\left(\frac{84}{85}\right) \), we will start from the left-hand side and simplify it step by step. ### Step 1: Use the formula for the difference of inverse sines We can use the formula: \[ \sin^{-1}(a) - \sin^{-1}(b) = \sin^{-1}(a\sqrt{1-b^2} - b\sqrt{1-a^2}) \] where \( a = \frac{3}{5} \) and \( b = \frac{8}{17} \). ...
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