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Question
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
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Solution
`sin^-1 8/17 + sin^-1 3/5`
= `tan^-1 8/sqrt(17^2 - 8^2) + tan^-1 3/sqrt(5^2 - 3^2) ...[sin^-1 p/h = tan^-1 p/sqrt(h^2 - p^2)]`
= `tan^-1 8/sqrt(289 - 64) + tan^-1 3/sqrt(25 - 9)`
= `tan^-1 8/sqrt225 + tan^-1 3/sqrt16`
= `tan^-1 8/15 + tan^-1 3/4`
= `tan^-1 ((8/15 + 3/4)/(1 - 8/15 xx 3/4)) ...[tan^-1x + tan^-1y = tan^-1((x + y)/(1 - x xx y))]`
= `tan^-1[((32 + 45)/60)/(1 - 24/60)]`
= `tan^-1 77/36`
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