Do \(-1\le sinx;cosx\le1\Rightarrow\left\{{}\begin{matrix}sin^{2022}x\le sin^2x\\cos^{2022}x\le cos^2x\end{matrix}\right.\)
\(\Rightarrow sin^{2022}x+cos^{2022}x\le sin^2x+cos^2x=1\)
\(\Rightarrow f\left(x\right)_{max}=1\)
Áp dụng BĐT: \(a^n+b^n\ge\left(\dfrac{a+b}{2}\right)^n\)
\(\Rightarrow\left(sin^2x\right)^{1011}+\left(cos^2x\right)^{1011}\ge\left(\dfrac{sin^2x+cos^2x}{2}\right)^{1011}=\dfrac{1}{2^{1011}}\)
\(\Rightarrow f\left(x\right)_{min}=\dfrac{1}{2^{1011}}\)
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