Rút gọn biểu thức A=sin2a+sin3a+sin4a/cos2a+cos3a+cos4a

$\begin{array}{l}
\dfrac{{\sin 2a + \sin 3a + \sin 4a}}{{\cos 2a + \cos 3a + \cos 4a}}\\
 = \dfrac{{\left( {\sin 2a + \sin 4a} \right) + \sin 3a}}{{\left( {\cos 2a + \cos 4a} \right) + \cos 3a}}\\
 = \dfrac{{2\sin 3a\cos a + \sin 3a}}{{2\cos 3a\cos a + \cos 3a}} = \dfrac{{\sin 3a\left( {2\cos a + 1} \right)}}{{\cos 3a\left( {2\cos a + 1} \right)}}\\
 = \dfrac{{\sin 3a}}{{\cos 3a}} = \tan 3a
\end{array}$