\(\Leftrightarrow\cot^22x=\tan^2x\)
\(\Leftrightarrow\tan^2\left(\dfrac{\Pi}{2}-2x\right)=\tan^2x\)
TH1: \(\tan\left(\dfrac{\Pi}{2}-2x\right)=\tan\left(x\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< >\dfrac{\Pi}{2}+k\Pi\\\dfrac{\Pi}{2}-2x=x+k\Pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< >\dfrac{\Pi}{2}+k\Pi\\-3x=k\Pi-\dfrac{\Pi}{2}\end{matrix}\right.\Leftrightarrow x=-\dfrac{1}{3}\left(k\Pi-\dfrac{\Pi}{2}\right)\)
TH2: \(\tan\left(\dfrac{\Pi}{2}-2x\right)=\tan\left(-x\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}-x< >\dfrac{\Pi}{2}+k\Pi\\\dfrac{\Pi}{2}-2x=-x+k\Pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< >-\dfrac{\Pi}{2}-k\Pi\\-x=k\Pi-\dfrac{\Pi}{2}\end{matrix}\right.\Leftrightarrow x=-k\Pi+\dfrac{\Pi}{2}\)
