Đáp án:
$\begin{array}{l}
Do:0 < a < \frac{\pi }{2}\\
\Rightarrow \sin a > 0\\
\Rightarrow \sin a = \sqrt {1 - {{\cos }^2}a} = \frac{4}{5}\\
\Rightarrow \tan a = \frac{{\sin a}}{{\cos a}} = \frac{4}{3}\\
+ )\cos \left( {a - \frac{\pi }{3}} \right)\\
= \cos a.\cos \frac{\pi }{3} + \sin a.\sin \frac{\pi }{3}\\
= \frac{3}{5}.\frac{1}{2} + \frac{4}{5}.\frac{{\sqrt 3 }}{2}\\
= \frac{{3 + 4\sqrt 3 }}{{10}}\\
+ )\tan \left( {a + \frac{\pi }{4}} \right)\\
= \frac{{\tan a + \tan \frac{\pi }{4}}}{{1 - \tan a.\tan \frac{\pi }{4}}} = 277,56
\end{array}$
