Lời giải:
$3\sin a-\cos a=\frac{1}{2}$
$\cos a=3\sin a-\frac{1}{2}$
$\cos ^2a=(3\sin a-\frac{1}{2})^2$
$1-\sin ^2a=9\sin ^2a-3\sin a+\frac{1}{4}$
$10\sin ^2a-3\sin a-\frac{3}{4}=0$
$\Rightarrow \sin a= \frac{3\pm \sqrt{39}}{20}$
$\Rightarrow \cos a=\frac{-1\pm 3\sqrt{39}}{20}$
$\Rightarrow \tan a=\frac{\sin a}{\cos a}=\frac{3+\sqrt{39}}{-1+3\sqrt{39}}$ hoặc $\tan a=\frac{3-\sqrt{39}}{-1-3\sqrt{39}}$
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