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Show that "cos"^(-1) 4/5+"sin"^(-1) 15/1...

Show that `"cos"^(-1) 4/5+"sin"^(-1) 15/17=(pi)/2+"cos"^(-1)84/85`

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Verified by Experts

`"cos"^(-1) 4/5="sin"^(-1)3/5`
`:' 3/5 gt 0, 15/17 gt0` and `(3/5)^(2)+(15/17)^(2)=8226/7225gt1`
`:. "sin"^(-1) 3/5+"sin"^(-1)15/17=pi-sin^(-1)(3/5sqrt(1-225/289)+15/17sqrt(1-9/25))`
`=pi-sin^(-1)(3/5 . 8/17+15/17 . 4/5)-pi-sin^(-1)(84/85)=pi-(pi)/2+"cos"^(-1) 84/85=(pi)/2+"cos"^(-1) 84/85`
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