Solve the equation on the interval $0 \leq θ < 2 π$ .
$\cos (2 θ) = \frac{\sqrt{3}}{2}$

What are the solutions to $\cos (2 θ) = \frac{\sqrt{3}}{2}$ in the interval $0 \leq θ < 2 π$ ? Select the correct choice and fill in any answer boxes in your choice below.
A. The solution set is \{\} .
(Simplify your answer. Type an exact answer, using $π$ as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. There is no solution.

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Final Answer: The solution set is ${\frac{π}{12}, \frac{11 π}{12}}$ .

Steps

Step 1 ：The given equation is in the form of $\cos (2 θ) = \frac{\sqrt{3}}{2}$ .

Step 2 ：We know that the cosine function has the value of $\frac{\sqrt{3}}{2}$ at $\frac{π}{6}$ and $\frac{11 π}{6}$ in the interval $0 \leq θ < 2 π$ .

Step 3 ：However, the angle in the cosine function is $2 θ$ not $θ$ . So, we need to solve the equations $2 θ = \frac{π}{6}$ and $2 θ = \frac{11 π}{6}$ to find the values of $θ$ in the interval $0 \leq θ < 2 π$ .

Step 4 ：The solutions to the equations $2 θ = \frac{π}{6}$ and $2 θ = \frac{11 π}{6}$ are $θ = \frac{π}{12}$ and $θ = \frac{11 π}{12}$ respectively.

Step 5 ：These are the solutions to the original equation $\cos (2 θ) = \frac{\sqrt{3}}{2}$ in the interval $0 \leq θ < 2 π$ .

Step 6 ：Final Answer: The solution set is ${\frac{π}{12}, \frac{11 π}{12}}$ .

Answer

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