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Question
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Solution
`tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`
`tan^(-1)b + tan^(-1) c = pi - tan^(-1) (a)`
`tan^(-1) ((b+c)/(1-bc)) = pi - tan^(-1) a`
`(b+c)/(1-bc) = tan(pi - tan^(-1) a)`
`(b + c)/(1-bc) = -tan(tan^(-1)a)`
`(b+c)/(1-bc) = -a`
b + c = -a + abc
`:. a + b + c = abc`
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