Cmr: (sin4a/1+cos4a)×(cos2a/1+cos2a)=tan a

Đáp án:

$\begin{array}{l}
\frac{{\sin 4a}}{{1 + \cos 4a}}.\frac{{\cos 2a}}{{1 + \cos 2a}}\\
 = \frac{{2.\sin 2a.\cos 2a}}{{2.{{\cos }^2}2a}}.\frac{{\cos 2a}}{{2{{\cos }^2}a}}\\
 = \frac{{\sin 2a}}{{2.{{\cos }^2}a}}\\
 = \frac{{2.\sin a.\cos a}}{{2.{{\cos }^2}a}}\\
 = \frac{{\sin a}}{{\cos a}}\\
 = \tan a
\end{array}$

Vậy $\frac{{\sin 4a}}{{1 + \cos 4a}}.\frac{{\cos 2a}}{{1 + \cos 2a}} = \tan a$