Đáp án:
\[A = \dfrac{{ - 12\sqrt 3 + 5}}{{26}}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{\pi }{2} < \dfrac{a}{2} < \dfrac{{3\pi }}{4} \Leftrightarrow \pi < a < \dfrac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin a < 0\\
\cos a < 0
\end{array} \right.\\
\sin a < 0 \Rightarrow \sin a = - \sqrt {1 - {{\cos }^2}a} = - \dfrac{5}{{13}}\\
A = \sin \left( {\dfrac{\pi }{3} - a} \right) = \sin \dfrac{\pi }{3}.\cos a - \sin a.\cos \dfrac{\pi }{3}\\
= \dfrac{{\sqrt 3 }}{2}.\dfrac{{ - 12}}{{13}} - \dfrac{{ - 5}}{{13}}.\dfrac{1}{2} = \dfrac{{ - 12\sqrt 3 + 5}}{{26}}
\end{array}\)
