Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{{3\pi }}{2} < a < 2\pi \Rightarrow \left\{ \begin{array}{l}
\cos a > 0\\
\sin a < 0
\end{array} \right.\\
{\sin ^2}a + {\cos ^2}a = 1\\
\sin a < 0 \Rightarrow \sin a = - \sqrt {1 - {{\cos }^2}a} = - \sqrt {1 - {{\left( {\frac{3}{5}} \right)}^2}} = - \frac{4}{5}\\
\cos \left( {a - \frac{{2\pi }}{3}} \right) = \cos a.\cos \frac{{2\pi }}{3} + \sin a.\sin \frac{{2\pi }}{3} = \frac{3}{5}.\left( { - \frac{1}{2}} \right) + \left( { - \frac{4}{5}} \right).\frac{{\sqrt 3 }}{2} = \frac{{ - 3 - 4\sqrt 3 }}{{10}}\\
\sin 4a = 2\sin 2a.\cos 2a = 2.2\sin a.\cos a.\left( {2{{\cos }^2}a - 1} \right) = 4.\left( { - \frac{4}{5}} \right).\left( {\frac{3}{5}} \right).\left( {2.{{\left( {\frac{3}{5}} \right)}^2} - 1} \right) = \frac{{336}}{{625}}
\end{array}\)
