31. D đúng
\(-1\le sin\le1\Rightarrow1\le2-sinx\le3\)
\(\Rightarrow y\ge\dfrac{2}{3}\)
\(y_{min}=\dfrac{2}{3}\) khi \(sinx=-1\)
\(\Rightarrow x=-\dfrac{\pi}{2}+k2\pi\)
32. A đúng
\(cos2x=2cosx-1\Leftrightarrow2cos^2x-1=2cosx-1\)
\(\Rightarrow cosx\left(cosx-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}cosx=0\\cosx=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=k2\pi\end{matrix}\right.\)
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