Prove the following results: tan^-1 1/7 + tan^-1 1/13 = tan^-1 2/9

Question

Prove the following results:

tan^-1\(\frac 17\) + tan^-1\(\frac{1}{13}\) = tan^-1\(\frac 29\)

Answer 1

Given:- tan^-1(\(\frac 17\)) + tan^-1(\(\frac{1}{13}\)) = tan^-1(\(\frac 29\))

Take

LHS

 tan^-1(\(\frac 17\)) + tan^-1(\(\frac{1}{13}\))

We know that, Formula