` cos^{2}x + cos^{2}2x + cos^{2}3x + cos^{2}4x = 2 `
`<=> cos²x+cos²2x+xos²3x+cos²4x=2`
`⇔2cos²x+2cos²2x+2cos²3x+2cos²4x=4`
`⇔ (2cos²x-1)+(2cos²2x-1)+(2cos²3x-1)+(2cos²4x-1)=0 `
`⇔cos2x+cos4x+cos6x+cos8x=0`
`⇔(cos2x+cos8x)+(cos4x+cos8x)=0`
`⇔1/2 cos5x.cos3x+1/2cosx.cos5x=0 `
`⇔1/2 cos5x(cos3x+cosx)=0`
` <=> cos5x(cos3x + cosx) = 0 `
` <=> `\(\left[ \begin{array}{l}cos5x=0\\cos3x+cosx=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\frac{π}{10}+\frac{kπ}{5}\\x=\frac{kπ}{2}+kπ\\x=\frac{π}{4}+\frac{kπ}{2}\end{array} \right.\) `(k ∈ Z)`
