solve-tan-1-2x-1-x-2-cot-1-1-x-2-2x-pi-3-

Question Number 27393 by kumar123 last updated on 06/Jan/18

s o l v e

\tan^{- 1} (2 x / 1 - x^{2}) + \cot^{- 1} (1 - x^{2} / 2 x) = π / 3

Answered by $@ty@m last updated on 06/Jan/18

L e t x = \tan u

\tan^{- 1} \frac{2 \tan u}{1 - \tan^{2} u} + \cot^{- 1} \frac{1 - \tan^{2} u}{2 \tan u} = \frac{π}{3}

\tan^{- 1} \tan 2 u + \cot^{- 1} \cot 2 u = \frac{π}{3}

2 u + 2 u = \frac{π}{3}

4 u = \frac{π}{3}

u = \frac{π}{12}

\tan^{- 1} x = \frac{π}{12}

x = \tan \frac{π}{12}

= 2 - \sqrt{3}

Facebook Tweet Pin