Đáp án:
$\begin{array}{l}
\sin a + \cos 2a = - 1\\
\Rightarrow \sin a + 1 - 2{\sin ^2}a = - 1\\
\Rightarrow 2{\sin ^2}a - \sin a - 2 = 0\\
\Rightarrow \left[ \begin{array}{l}
\sin a = \dfrac{{1 + \sqrt {17} }}{4}\left( {ktm} \right)\\
\sin a = \dfrac{{1 - \sqrt {17} }}{4}\left( {tm} \right)
\end{array} \right.\\
Do:{90^0} < a < {180^0}\\
\Rightarrow \cos a < 0\\
\Rightarrow \cos a = - \sqrt {1 - {{\sin }^2}a} = - 0,625\\
\Rightarrow \sin 2a = 2.\sin a.\cos a = 0,976
\end{array}$