\(A=6\left(1-sin^2x\right)+6sinx-2=-6sin^2x+6sinx+4\)
Đặt \(sinx=a\Rightarrow-1\le a\le1\) \(\Rightarrow A=-6a^2+6a+4\)
\(A\left(-1\right)=-8\) ; \(A\left(1\right)=4\); \(A\left(\frac{1}{2}\right)=\frac{11}{2}\)
\(\Rightarrow A_{max}=\frac{11}{2}\) khi \(a=\frac{1}{2}\Leftrightarrow sinx=\frac{1}{2}\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+k2\pi\\x=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(A_{min}=-8\) khi \(a=-1\Leftrightarrow sinx=-1\Rightarrow x=-\frac{\pi}{2}+k2\pi\)
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