Chứng minh rằng: tan 2a/ tan 4a - tan 2a = cos 4a.

\(\frac{{\cos 2a.\tan 2a}}{{\cos 2a\left( {\tan 4a - \tan 2a} \right)}}\)

\( = \frac{{\sin 2a}}{{\frac{{\cos 2a.\sin 4a}}{{\cos 4a}} - \sin 2a}}\)

\( = \frac{{\cos 4a.\sin 2a}}{{\sin 4a.\cos 2a - \sin 2a.\cos 4a}}\)

\( = \frac{{\cos 4a.\sin 2a}}{{\sin \left( {4a - 2a} \right)}}\)

\( = \frac{{\cos 4a.\sin 2a}}{{\sin 2a}}\)

= cos4a.