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Điều kiện $\cos x \ne 0.$
PT
$\Leftrightarrow \sin^{2}x(\tan x +1) = 3\sin x\cos x+3(1-\sin^2 x)$
$\Leftrightarrow \sin^{2}x(\tan x +1) = 3\sin x\cos x+3\cos^2 x$
$\Leftrightarrow \sin^{2}x(\tan x +1) = 3\cos x(\sin x+ \cos x)$
$\Leftrightarrow \sin^{2}x(\tan x\cos x +\cos x) = 3\cos^2 x(\sin x+ \cos x)$
$\Leftrightarrow \sin^{2}x(\sin x +\cos x) = 3\cos^2 x(\sin x+ \cos x)$
$\Leftrightarrow \left[ {\begin{matrix} \sin x +\cos x=0\\ \sin^{2}x=3\cos^2 x \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} \sin x +\cos x=0\\ 1=4\cos^2 x \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} \sin x +\cos x=0\\ \cos^2 x=1/4 \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} \sin x +\cos x=0\\ \cos x=\pm 1/2 \end{matrix}} \right.$
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