Nhận thấy \(cos\frac{x}{2}=0\) ko phải nghiệm, chia 2 vế cho \(cos^3\frac{x}{2}\) ta được:
\(3tan^3\frac{x}{2}+3tan^2\frac{x}{2}=tan\frac{x}{2}+1\)
\(\Leftrightarrow3tan^2\frac{x}{2}\left(tan\frac{x}{2}+1\right)-\left(tan\frac{x}{2}+1\right)=0\)
\(\Leftrightarrow\left(3tan^2\frac{x}{2}-1\right)\left(tan\frac{x}{2}+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tan\frac{x}{2}=-1\\tan\frac{x}{2}=\frac{1}{\sqrt{3}}\\tan\frac{x}{2}=-\frac{1}{\sqrt{3}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{2}+k2\pi\\x=\frac{\pi}{3}+k2\pi\\x=-\frac{\pi}{3}+k2\pi\end{matrix}\right.\)
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