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Ta có:
$\sqrt{7+4\sqrt{3} }^{\sin x}+\sqrt{7-4\sqrt{3} }^{\sin x} =4$
$\Leftrightarrow (2+\sqrt3)^{\sin x}+
(2-\sqrt3)^{\sin x}=4$
$\Leftrightarrow
(2+\sqrt3)^{2\sin x}+1=4.(2+\sqrt3)^{\sin x} $
$\Leftrightarrow
\left[ \begin{array}{l}
(2+\sqrt3)^{\sin x}=2+\sqrt3\\
(2+\sqrt3)^{\sin x}=
2-\sqrt3 \end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l} \sin x=1\\ \sin x=-1 \end{array} \right.$
$\Leftrightarrow \cos x=0 \Leftrightarrow x=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$ .
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