Với \(cosx=0\) ko phải nghiệm
Với \(cosx\ne0\) chia 2 vế cho \(cos^3x\)
\(\Rightarrow1-4tan^3x-3tan^2x+tanx.\dfrac{1}{cos^2x}=0\)
\(\Leftrightarrow1-4tan^3x-3tan^2x+tanx\left(1+tan^2x\right)=0\)
\(\Leftrightarrow-3tan^3x-3tan^2x+tanx+1=0\)
\(\Leftrightarrow-3tan^2x\left(tanx+1\right)+tanx+1=0\)
\(\Leftrightarrow\left(tanx+1\right)\left(1-3tan^2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=-1\\tanx=\dfrac{1}{\sqrt{3}}\\tanx=-\dfrac{1}{\sqrt{3}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k\pi\\x=\dfrac{\pi}{6}+k\pi\\x=-\dfrac{\pi}{6}+k\pi\end{matrix}\right.\)
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