\(A=\left(\dfrac{1-cos2x}{2}\right)^2+2\left(\dfrac{1+cos2x}{2}\right)^2\)
\(=\dfrac{3}{4}cos^22x+\dfrac{1}{2}cos2x+\dfrac{3}{4}\)
\(A=\dfrac{1}{12}\left(3cos2x+1\right)^2+\dfrac{2}{3}\ge\dfrac{2}{3}\)
\(A_{min}=\dfrac{2}{3}\) khi \(cos2x=-\dfrac{1}{3}\)
\(A=\dfrac{3cos^22x+2cos2x-5}{4}+2=\dfrac{\left(3cos2x+5\right)\left(cos2x-1\right)}{4}+2\le2\)
\(A_{max}=2\) khi \(cos2x=1\)
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