-1 \end{cases}\Rightarrow\begin{cases}\cos2x<0 \\\cos2x>-2 \end{cases}\Rightarrow\cos2x<0\\ \frac\pi2+2\pi n<2x<\frac{3\pi}2+2\pi n\\\frac{\pi}4+\pi n<x<\frac{3\pi}4+\pi n,\;\;n\in\mathbb{Z}" alt="|cos2x+1|<1\\\begin{cases}\cos2x+1<1 \\\cos2x+1>-1 \end{cases}\Rightarrow\begin{cases}\cos2x<0 \\\cos2x>-2 \end{cases}\Rightarrow\cos2x<0\\ \frac\pi2+2\pi n<2x<\frac{3\pi}2+2\pi n\\\frac{\pi}4+\pi n<x<\frac{3\pi}4+\pi n,\;\;n\in\mathbb{Z}" align="absmiddle" class="latex-formula">