\(DKXD:\left\{{}\begin{matrix}\sin x\ne0\\\cos x\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne\pi+k\pi\\x\ne\frac{\pi}{2}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\tan x+\frac{\sqrt{3}}{\tan x}-\left(\sqrt{3}+1\right)=0\)
\(\Leftrightarrow\tan^2x-\left(\sqrt{3}+1\right)\tan x+\sqrt{3}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\tan x=1\\\tan x=\sqrt{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k\pi\\x=\frac{\pi}{3}+k\pi\end{matrix}\right.\) (t/m)
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