Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
b,\\
\sin x + \sin y = 2.\sin \frac{{x + y}}{2}.\cos \frac{{x - y}}{2}\\
\cos x + \cos y = 2\cos \frac{{x + y}}{2}.cos\frac{{x - y}}{2}\\
\frac{{\sin a + \sin 3a + \sin 5a}}{{\cos a + \cos 3a + \cos 5a}}\\
= \frac{{\left( {\sin a + \sin 5a} \right) + \sin 3a}}{{\left( {\cos a + \cos 5a} \right) + \cos 3a}}\\
= \frac{{2\sin 3a.\cos 2a + \sin 3a}}{{2.cos3a.\cos 2a + \cos 3a}}\\
= \frac{{\sin 3a\left( {2\cos 2a + 1} \right)}}{{\cos 3a.\left( {2\cos 2a + 1} \right)}}\\
= \frac{{\sin 3a}}{{\cos 3a}} = \tan 3a\\
c,\\
\sin x - \sin y = 2\cos \frac{{x + y}}{2}.\sin \frac{{x - y}}{2}\\
\frac{{\sin 5a - sin3a}}{{2\sin 4a}} = \frac{{2.\cos 4a.\sin a}}{{2\sin 4a}} = \cot 4a.\sin a
\end{array}\)
