Question

tan^-1(1+x/1-x)= π\4+ tan^-1 x...pls solve for x​

Answer 1

Answer:

tan -1 (1 + x/ 1 – x) = π/4 + tan -1 x, x < 1 Consider x = tan θ Where θ = tan -1 x Here LHS = tan -1 (1 + x/ 1 – x) By substituting the value = tan -1 (1 + tan θ/ 1 – tan θ) = tan -1 (tan [π/4 + θ]) So we get = π/4 + θ By substituting the value of θ = π/4 + tan -1 x = RHS Hence, it is proved.Read more on Sarthaks.com - https://www.sarthaks.com/757474/prove-that-tan-1-1-x-1-x-4-tan-1x-x-1?show=757482#a757482