Cho \(\sin a =  - \frac{{12}}{{13}};\,\,\frac{{3\pi }}{2} v...

* Hướng dẫn giải

\(\begin{array}{l}
\cos a = \sqrt {1 - {{\sin }^2}a}  = \frac{5}{{13}}\left( {\,\,\frac{{3\pi }}{2} < a < 2\pi } \right)\\
 \Rightarrow \cos \left( {\frac{\pi }{3} - a} \right) = \cos \frac{\pi }{3}.\cos a + \sin \frac{\pi }{3}.\sin a\\
 = \frac{1}{2}.\frac{5}{{13}} + \frac{{\sqrt 3 }}{2}.\left( { - \frac{{12}}{{13}}} \right) = \frac{{5 - 12\sqrt 3 }}{{26}}
\end{array}\)