Prove that `tan^(-1)3/4+tan^(-1)3/5-tan^(-1)8/19=pi/4`.

1.	Prove that `tan^(-1)3/4+tan^(-1)3/5-tan^(-1)8/19=pi/4`.
Answer» We have, LHS `={tan^(-1)3/4+tan^(-1)3/5}-tan^(-1)8/19` `=tan^(-1){((3/4+3/5)/(1-3/4 xx 3/5))}-tan^(-1) 8/19` `=tan^(-1)(27/1)-tan^(-1)8/19` `=tan^(-1)((27/11-8/19))/(1+27/11 xx 8/9))=tan^(-1)(425/425) = tan^(-1)=pi/4` =RHS. `therefore` LHS=RHS.

Discussion

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