`2sin x - sqrt{3} = 0`
`<=> sin x = (\sqrt{3})/2`
`<=>` \(\left[ \begin{array}{l}x = \dfrac{π}{3} + k2π\\x = \dfrac{2π}{3} + k2π\end{array} \right.\)
Vì `x ∈ [0; 2π]`
`=>` \(\left[ \begin{array}{l}0 ≤ \dfrac{π}{3} + k2π ≤ 2π\\0 ≤ \dfrac{2π}{3} + k2π ≤ 2π\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}-\dfrac{π}{3} ≤ k2π ≤ \dfrac{5π}{3}\\-\dfrac{2π}{3} ≤ k2π ≤ \dfrac{4π}{3} \end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}-\dfrac{1}{6} ≤ k ≤ \dfrac{5}{6}\\-\dfrac{1}{3} ≤ k ≤ \dfrac{2}{3}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}-0,17 ≤ k ≤ 0,8\\-0,3 ≤ k ≤ 0,7\end{array} \right.\)
`=> k ∈ {0}`
Vậy số nghiệm của phương trình là:
\(\left[ \begin{array}{l}x = \dfrac{π}{3}\\x = \dfrac{2π}{3}\end{array} \right.\)
