ĐKXĐ: \(\left\{{}\begin{matrix}cosx\ne0\\cos2x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{2}+k\pi\\x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\end{matrix}\right.\)
\(\dfrac{3sin2x}{cos2x}-3tanx-\dfrac{5}{2}=0\)
\(\Leftrightarrow\dfrac{6sinx.cosx}{cos^2x-sin^2x}-3tanx-\dfrac{5}{2}=0\)
\(\Rightarrow\dfrac{6tanx}{1-tan^2x}-3tanx-\dfrac{5}{2}=0\)
\(\Rightarrow6tan^3x+5tan^2x+6tanx-5=0\)
\(\Leftrightarrow\left(2tanx-1\right)\left(3tan^2x+4tanx+5\right)=0\)
\(\Leftrightarrow tanx=\dfrac{1}{2}\)
\(\Leftrightarrow x=arctan\left(\dfrac{1}{2}\right)+k\pi\)
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