a/ \(x\in\left(-\frac{\pi}{3};\frac{2\pi}{3}\right)\Rightarrow-\frac{\sqrt{3}}{2}< sinx\le1\)
\(\Rightarrow0\le sin^2x\le1\)
\(\Rightarrow-1\le3-4sin^2x\le3\)
\(y_{min}=-1\) khi \(x=\frac{\pi}{2}\)
\(y_{max}=3\) khi \(x=0\)
b/ \(y=cos^2x-2\left(2cos^2x-1\right)=2-3cos^2x\)
\(\frac{\pi}{6}\le x\le\frac{7\pi}{6}\Rightarrow-1\le cosx\le\frac{\sqrt{3}}{2}\Rightarrow0\le cos^2x\le1\)
\(\Rightarrow-1\le2-3cos^2x\le2\)
\(y_{min}=-1\) khi \(x=\pi\)
\(y_{max}=2\) khi \(x=\frac{\pi}{2}\)
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