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प्रश्न
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
उत्तर
`sin^-1 8/17 + sin^-1 3/5 = tan^-1 8/sqrt(17^2 - 8^2) + tan^2 3/sqrt(5^2 - 3^2)` ...`[sin^-1 "p"/"h" = tan^-1 "p"/sqrt("h"^2 - "p"^2)]`
= `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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