\(\Leftrightarrow4sin^{2020}x\left(1-2sin^2x\right)=4cos^{2020}x\left(2cos^2x-1\right)+5cos2x=0\)
\(\Leftrightarrow4sin^{2020}x.cos2x=4cos^{2020}x.cos2x+5cos2x\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\Rightarrow x=...\\4sin^{2020}x=4cos^{2020}x+5\left(1\right)\end{matrix}\right.\)
Xét (1), ta có \(\left\{{}\begin{matrix}4sin^{2020}x\le4\\4cos^{2020}x+5\ge5\end{matrix}\right.\)
\(\Rightarrow4sin^{2020}x< 4cos^{2020}x+5\) với mọi x
\(\Rightarrow\left(1\right)\) vô nghiệm
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