Tính tan2α.

D

\(\tan \left( {\alpha  - \frac{\pi }{4}} \right) = 3\) \( \Leftrightarrow \frac{{\tan \alpha  - \tan \frac{\pi }{4}}}{{1 + \tan \alpha \tan \frac{\pi }{4}}} = 3\)\( \Leftrightarrow \frac{{\tan \alpha  - 1}}{{1 + \tan \alpha }} = 3\)\( \Leftrightarrow \tan \alpha  =  - 2\).

Khi đó \(\tan 2\alpha  = \frac{{2\tan \alpha }}{{1 - {{\tan }^2}\alpha }} = \frac{{2.\left( { - 2} \right)}}{{1 - {{\left( { - 2} \right)}^2}}} = \frac{4}{3}\).