Question

\(3tanx+\sqrt{3}cotx-3-\sqrt{3}=0\)

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Answer 1

ĐKXĐ: \(sin2x\ne0\Rightarrow x\ne\dfrac{k\pi}{2}\)

\(3tanx+\dfrac{\sqrt{3}}{tanx}-3-\sqrt{3}=0\)

\(\Rightarrow3tan^2x-\left(3+\sqrt{3}\right)tanx+\sqrt{3}=0\)

\(\Rightarrow\left[{}\begin{matrix}tanx=1\\tanx=\dfrac{\sqrt{3}}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k\pi\\x=\dfrac{\pi}{6}+k\pi\end{matrix}\right.\)