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Prove that:sin^(-1)8/(17)+sin^(-1)3/5=ta...

Prove that:`sin^(-1)8/(17)+sin^(-1)3/5=tan^(-1)(77)/(36)`

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LHS=`sin^(-1)""(8)/(17)+sin^(-1)""(3)/(5)`
`=sin^(-1)""[(8)/(17)sqrt(1-((3)/(4))^(2))+(3)/(5)sqrt(1-((8)/(17))^(2))]`
`=sin^(-1)[(8)/(17)xx(4)/(5)+(3)/(5)xx(15)/(17)]`
`( :.sin^(1)x=tan^(-1)""(x)/(sqrt(1-x^(2))))`
`=sin^(-1)""(77)/(85)=tan^(-1)""(77//85)/(sqrt(1-((77)/(85))^(2)))`
`tan^(-1)((77//875)/(36//85))=tan^(-1)""(77)/(36)`= RHS Hence proved.
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