Đáp án:
\(\dfrac{{\sqrt 2 }}{{10}}\)
Giải thích các bước giải:
\(\begin{array}{l}
Có:\\
{\sin ^2}a + {\cos ^2}a = 1\\
\to {\sin ^2}a + \dfrac{{16}}{{25}} = 1\\
\to {\sin ^2}a = \dfrac{9}{{25}}\\
Do:a \in \left( {\pi ;\dfrac{{3\pi }}{2}} \right)\\
\to \sin a < 0\\
\to \sin a = - \dfrac{3}{5}\\
\sin \left( {a - \dfrac{\pi }{4}} \right) = \sin a.\cos \dfrac{\pi }{4} - \cos a.\sin \dfrac{\pi }{4}\\
= - \dfrac{3}{5}.\dfrac{{\sqrt 2 }}{2} + \dfrac{4}{5}.\dfrac{{\sqrt 2 }}{2} = \dfrac{{\sqrt 2 }}{{10}}
\end{array}\)
