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Question
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
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Solution
Tp prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
L.H.S = `2tan^(-1) 1/2 + tan^(-1) 1/7`
= `tan^(-1) (2. 1/2)/(1-(1/2)^2) + tan^(-1) 1/7` ` " "[2 tan^(-1) x = tan^(-1) (2x)/(1-x^2)]`
`= tan^(-1) 1/ ((3/4)) + tan^(-1) 1/7`
`= tan^(-1) 4/3 + tan^(-1) 1/7`
= `tan^(-1) (4/3 + 1/7) /(1 - 4/3. 1/7)` `[tan^(-1) x + tan^(-1) y = tan^(-1) (x + y)/(1 - xy)]`
`= tan^(-1) ((28+3)/21)/((21-4)/21)`
= `tan^(-1) 31/17` = R.H.S
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