$\Leftrightarrow\left[\begin{array}{I} \cos x+\sin x=0\\ \cos x-\sin x =1\end{array}\right.\Leftrightarrow\left[\begin{array}{I} \tan x=-1\\ \cos(x+\frac{\pi}{4})=\frac{1}{\sqrt{2}}\end{array}\right.$
$\Leftrightarrow\left[\begin{array}{I} x=\frac{-\pi}{4}+k\pi\\ x=k2\pi\\ x=\frac{-\pi}{2}+k2\pi\end{array}\right., k\in Z$
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