a/
ĐKXĐ: ...
\(\Leftrightarrow tanx-8\sqrt{3}=3tanx-6\sqrt{3}\)
\(\Leftrightarrow2tanx=-2\sqrt{3}\)
\(\Rightarrow tanx=-\sqrt{3}\Rightarrow x=-\frac{\pi}{3}+k\pi\)
b/
\(\Leftrightarrow tan2x=-cot\left(\frac{5\pi}{8}\right)\)
\(\Leftrightarrow tan2x=tan\left(\frac{\pi}{2}+\frac{5\pi}{8}\right)\)
\(\Leftrightarrow tan2x=tan\left(\frac{9\pi}{8}\right)\)
\(\Rightarrow2x=\frac{9\pi}{8}+k\pi\Rightarrow x=\frac{9\pi}{16}+\frac{k\pi}{2}\)
c/
\(\Leftrightarrow\sqrt{3}tan\left(\frac{\pi}{9}-2x\right)=-3\)
\(\Leftrightarrow tan\left(\frac{\pi}{9}-2x\right)=-\sqrt{3}\)
\(\Rightarrow\frac{\pi}{9}-2x=-\frac{\pi}{3}+k\pi\)
\(\Rightarrow x=\frac{2\pi}{9}+\frac{k\pi}{2}\)
d/
\(\Leftrightarrow\left[{}\begin{matrix}tanx=5\\tan2x=tan4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=arctan\left(5\right)+k\pi\\2x=4+k\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=arctan\left(5\right)+k\pi\\x=2+\frac{k\pi}{2}\end{matrix}\right.\)