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Question: \[\tan\left\lbrack 2\tan^{- 1}\left( \frac{1}{5} \right) - \frac{\pi}{4} \right\rbrack =\]...

tan⁡[2tan⁡−1(15)−π4]=\tan\left\lbrack 2\tan^{- 1}\left( \frac{1}{5} \right) - \frac{\pi}{4} \right\rbrack =

A

177\frac{17}{7}

B

−177- \frac{17}{7}

C

717\frac{7}{17}

D

−717- \frac{7}{17}

Answer

−717- \frac{7}{17}

Explanation

Solution

tan⁡[2tan⁡−1(15)−π4]=tan⁡[tan⁡−1251−125−tan⁡−1(1)]\tan\left\lbrack 2\tan^{- 1}\left( \frac{1}{5} \right) - \frac{\pi}{4} \right\rbrack = \tan\left\lbrack \tan^{- 1}\frac{\frac{2}{5}}{1 - \frac{1}{25}} - \tan^{- 1}(1) \right\rbrack

= tan⁡[tan⁡−1512−tan⁡−1(1)]=tan.tan−1(512−11+512)=−717\tan\left\lbrack \tan^{- 1}\frac{5}{12} - \tan^{- 1}(1) \right\rbrack = {tan.tan}^{- 1}\left( \frac{\frac{5}{12} - 1}{1 + \frac{5}{12}} \right) = \frac{- 7}{17}