Respuesta :

Subtracting 1 to the given equation we get:

[tex]\begin{gathered} 1-\cos \theta-1=\frac{2-\sqrt[]{3}}{2}-1, \\ -\text{cos}\theta=-\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}[/tex]

Multiplying by -1 we get:

[tex]\begin{gathered} -\cos \theta\cdot(-1)=-\frac{\sqrt[]{3}}{2}\cdot(-1), \\ \cos \theta=\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}[/tex]

Now, notice that:

[tex]\begin{gathered} \cos (\frac{\pi}{6}+2n\pi)=\frac{\sqrt[]{3}}{2}, \\ \cos (\frac{11\pi}{6}+2n\pi)=\frac{\sqrt[]{3}}{2}\text{.} \end{gathered}[/tex]

Therefore the solutions of the given equation in the interval [0,2π] are:

[tex]\frac{\pi}{6},\frac{11\pi}{6}.[/tex]

Answer: Option C.