`ĐK:`
\(\left[ \begin{array}{l}cos x \ne 0\\\sqrt{3}tan x - 1 \ne 0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x \ne \dfrac{\pi}{2} + kπ\\x \ne \dfrac{π}{6} + kπ\end{array} \right.\)
`PT`
`<=> 2cos² x + cos 2x - 2 = 0`
`<=> 2cos² x + 2cos² x - 1 - 2 = 0`
`<=> 4cos² x - 3 = 0`
`<=> cos² x = 3/4`
`<=> (1 + cos 2x)/2 = 3/4`
`<=> 1 + cos 2x = 3/2`
`<=> cos 2x = 1/2`
`<=> 2x = ±(π)/3 + k2π`
`<=> x = ±(π)/6 + kπ`
`=> x = -π/6 + kπ`
Vì `x ∈ (0; 2π)`
`=> 0 < x < 2π`
`<=> 0 < -π/6 + kπ < 2π`
`<=> π/6 < kπ < (13π)/6`
`<=> 1/6 < k < 13/6`
`<=> 0,17 < k < 2,17`
`=> k ∈ {1; 2}`
`=>` \(\left\{ \begin{array}{l}x = \dfrac{5π}{6}\\x = \dfrac{11π}{6}\end{array} \right.\)
`=>` Tổng tất cả các nghiệm là: `(5π)/6 + (11π)/6 = (8π)/3`
