\(\dfrac{\pi}{2}< a< \pi\Rightarrow\left\{{}\begin{matrix}sina>0\\cosa< 0\end{matrix}\right.\)
\(\left\{{}\begin{matrix}sina+2cosa=-1\\sin^2a+cos^2a=1\end{matrix}\right.\) \(\Rightarrow\left(-1-2cosa\right)^2+cos^2a=1\)
\(\Leftrightarrow5cos^2a+4cosa=0\Rightarrow\left[{}\begin{matrix}cosa=0\left(loại\right)\\cosa=-\dfrac{4}{5}\end{matrix}\right.\)
\(\Rightarrow sina=\sqrt{1-cos^2a}=\dfrac{3}{5}\)
\(sin2a=2sina.cosa=2.\left(-\dfrac{4}{5}\right).\left(\dfrac{3}{5}\right)=-\dfrac{24}{25}\)
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