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Question
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solution
`cos(sin^-1 3/5+sin^-1 5/13)=cos{sin^-1(3/5sqrt(1-(5/13)^2)+5/13sqrt(1-(3/5)^2))}`
`=cos{sin^-1(3/5xx12/13+5/13xx4/5)}`
`=cos{sin^-1(36/65+4/13)}`
`=cos{sin^-1(56/65)}`
`=cos{cos^-1sqrt(1-(56/65)^2)}` `[because sin^-1x=cos^-1sqrt(1-x^2)]`
`=cos{cos^-1 33/65}`
`=33/65`
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