ĐK: \(sin2x\ne0\Leftrightarrow x\ne k\frac{\pi}{2}\)
(*)\(\Leftrightarrow1+cot2x=\frac{1-cos2x}{1-cos^22x}\Leftrightarrow1+cot2x=\frac{1}{1+cos2x}\Leftrightarrow1+\frac{cos2x}{sin2x}=\frac{1}{1+cos2x}\)\(\Leftrightarrow sin2x\left(1+cos2x\right)+cos2x\left(1+cos2x\right)=sin2x\)
\(\Leftrightarrow sin2xcos2x+cos2x\left(1+cos2x\right)=0\Leftrightarrow cos2x\left(sin2x+cos2x+1\right)=0\)\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\sin2x+cos2x=-1\end{matrix}\right.\)
+\(cos2x=0\Leftrightarrow x=\frac{\pi}{4}+k\frac{\pi}{2}\)
+\(sin2x+cos2x=-1\Leftrightarrow sin\left(2x+\frac{\pi}{4}\right)=sin\left(-\frac{\pi}{4}\right)\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{4}+k\pi\\x=\frac{\pi}{2}+k\pi\end{matrix}\right.\)
