d, ĐK: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(tan^3x+tan^2x+tanx-3=0\)
\(\Leftrightarrow\left(tanx-1\right)\left(tan^2x+2tanx+3\right)=0\)
\(\Leftrightarrow tanx-1=0\)
\(\Leftrightarrow tanx=\text{}1\)
\(\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\)
e, \(x\ne\dfrac{\pi}{2}+k\pi\)
\(tan^3x-tanx=0\)
\(\Leftrightarrow tanx\left(tanx-1\right)\left(tanx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=0\\tanx=1\\tanx=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{\pi}{4}+k\pi\\x=-\dfrac{\pi}{4}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\pm\dfrac{\pi}{4}+k\pi\end{matrix}\right.\)
f, ĐK: \(x\ne\dfrac{k\pi}{2}\)
\(tan^3x+\dfrac{1}{cos^2x}-3cot\left(\dfrac{\pi}{2}-x\right)=4\)
\(\Leftrightarrow tan^3x+tan^2x+1-3tanx=4\)
\(\Leftrightarrow tan^3x+tan^2x-3tanx-3=0\)
\(\Leftrightarrow\left(tanx+1\right)\left(tan^2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=-1\\tanx=\pm\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k\pi\\x=\pm\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)
