Question

Solve on the interval [0,21): 2-3 1 - cos 9 = 2 O A. O B. *** 3 Oc. 7 117 6 7 T 11T O D.

Answer 1

Subtracting 1 to the given equation we get:

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

Multiplying by -1 we get:

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

Now, notice that:

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

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

`(\pi)/(6),(11\pi)/(6).`

Answer: Option C.