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Prove that : tan^(-1)(1/7)+tan^(-1)(1/(1...

Prove that : `tan^(-1)(1/7)+tan^(-1)(1/(13))=tan^(-1)(2/9)`

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LHS `= tan^ (-1)(1/7) + tan^ (-1)(1/13)`

`tan^ (-1)x + tan^ (-1)y = tan^ (-1) ((x + y )/ (1 - xy ))`

`xy < 1`

` tan^ (-1)(1/7) + tan^ (-1)(1/13)`

`= tan^ (-1)[(1/7 + 1/13)/ ((1 - 1/7 × 1/13) )]`

`= tan^ (-1)( ((13 + 7)/91 )/ ((7 × 13 (-1))/(7 × 13 ))) = X`

`= tan^ (-1) ((20 )/ (91 - 1 ))`

`= tan^ (-1)(2/9) =` RHS
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