Rút gọn biểu thức A

D

\(A = \frac{{\sin a + \sin 3a + \sin 5a}}{{\cos a + \cos 3a + \cos 5a}}\)\( = \frac{{\left( {\sin a + \sin 5a} \right) + \sin 3a}}{{\left( {\cos a + \cos 5a} \right) + \cos 3a}}\)\( = \frac{{2\sin 3a\cos 2a + \sin 3a}}{{2\cos 3a\cos 2a + \cos 3a}}\)

\( = \frac{{\sin 3a\left( {2\cos 2a + 1} \right)}}{{\cos 3a\left( {2\cos 2a + 1} \right)}}\)\( = \tan 3a\).