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PT
$\Leftrightarrow \dfrac{(\sin \dfrac{x}{2} -\cos \dfrac{x}{2})(\sin^2 \dfrac{x}{2} +\cos^2 \dfrac{x}{2}+\sin \dfrac{x}{2}\cos \dfrac{x}{2})}{2+\sin x} = \dfrac{1}{3}\left ( \cos \dfrac{x}{2} - \sin \dfrac{x}{2} \right )\left ( \cos \dfrac{x}{2} + \sin \dfrac{x}{2} \right ) $
$\Leftrightarrow \dfrac{(\sin \dfrac{x}{2} -\cos \dfrac{x}{2})(2+2\sin \dfrac{x}{2}\cos
\dfrac{x}{2})}{2(2+\sin x)} + \dfrac{1}{3}\left ( \sin \dfrac{x}{2} -\cos \dfrac{x}{2}\right )\left ( \cos \dfrac{x}{2} + \sin \dfrac{x}{2}
\right ) =0$
$\Leftrightarrow \dfrac{(\sin \dfrac{x}{2} -\cos \dfrac{x}{2})(2+2\sin x)}{2(2+\sin x)} + \dfrac{1}{3}\left ( \sin \dfrac{x}{2}
-\cos \dfrac{x}{2}\right )\left ( \cos \dfrac{x}{2} + \sin \dfrac{x}{2}
\right ) =0$
$\Leftrightarrow \dfrac{1}{2}\left ( \sin \dfrac{x}{2}
-\cos \dfrac{x}{2}\right )+ \dfrac{1}{3}\left ( \sin \dfrac{x}{2}
-\cos \dfrac{x}{2}\right )\left ( \cos \dfrac{x}{2} + \sin \dfrac{x}{2}
\right ) =0$
$\Leftrightarrow \left[ {\begin{matrix} \sin \dfrac{x}{2}=\cos \dfrac{x}{2}\\\\ \sin \dfrac{x}{2} +\cos \dfrac{x}{2}=-3/2 <-1 \text{(loại)}\end{matrix}} \right.$
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