The-value-of-tan-1-1-2-tan-1-1-3-is-

Question Number 49751 by Pk1167156@gmail.com last updated on 10/Dec/18

The value of \tan^{- 1} \frac{1}{2} + \tan^{- 1} \frac{1}{3} is

Commented by maxmathsup by imad last updated on 10/Dec/18

w e h a v e t a n (a r c t a n (\frac{1}{2}) + a r c t a n (\frac{1}{3})) =

= \frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} . \frac{1}{3}} = \frac{\frac{5}{6}}{\frac{5}{6}} = 1 \Rightarrow a r c t a n (\frac{1}{2}) + a r c t a n (\frac{1}{3}) = a r c t a n (1) = \frac{π}{4}

Answered by tanmay.chaudhury50@gmail.com last updated on 10/Dec/18

{t a n}^{- 1} (\frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} \times \frac{1}{3}}) = {t a n}^{- 1} (\frac{\frac{5}{6}}{\frac{5}{6}}) = {t a n}^{- 1} (1) = \frac{π}{4}