Prove that `2(tan^(-1)1/4+tan^(-1)2/9)=tan^(-1)4/3`.

1.	Prove that `2(tan^(-1)1/4+tan^(-1)2/9)=tan^(-1)4/3`.
Answer» We have, LHS =`2tan^(-1)1/4+2tan^(-1)2/9` `=tan^(-1)((2 xx 1/4)/(1-(1/4)^(2)) + tan^(-1)((2 xx 2/9)/(1-(2/9)^(2))` `=tan^(-1)((1/2)/(15/16))+tan^(-1)((4/9)/(77/81))` `=tan^(-1)(1/2 xx 16/15)+tan^(-1)(4/9xx 81/77)` `=tan^(-1)8/15+tan^(-1)36/77` `=tan^(-1)(1156)/867)=tan^(-1)4/3`=RHS `therefore` LHS=RHS.

Discussion

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