\(sin^8x+cos^8x=\left(sin^4x+cos^4x\right)^2-2sin^4x.cos^4x\)
\(=\left[\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x\right]^2-2\left(sinx.cosx\right)^4\)
\(=\left[1-\frac{1}{2}sin^22x\right]^2-\frac{1}{8}sin^42x\)
\(=1-sin^22x+\frac{1}{8}sin^42x=1-\frac{1-cos4x}{2}+\frac{1}{8}\left(\frac{1-cos4x}{2}\right)^2\)
\(=\frac{35}{64}+\frac{7}{16}cos4x+\frac{1}{64}cos8x\)
Pt đã cho trở thành:
\(\frac{35}{64}+\frac{7}{16}cos4x+\frac{65}{64}cos8x=2\)
\(\Leftrightarrow\frac{65}{64}\left(2cos^24x-1\right)+\frac{7}{16}cos4x-\frac{93}{64}=0\)
\(\Leftrightarrow130cos^24x+28cos4x-158=0\)
\(\Rightarrow\left[{}\begin{matrix}cos4x=1\\cos4x=-\frac{158}{130}< -1\left(l\right)\end{matrix}\right.\)
\(\Rightarrow4x=k2\pi\Rightarrow x=\frac{k\pi}{2}\)
