2 cos(2𝜃) − 1 = 0. Find the solutions in the interval [0, 2𝜋)

Answer 1

2cos(2θ) = 1

cos(2θ) = 1/2

2θ = π/3 + 2kπ or 5π/3 + 2kπ, where k = 0, 1, -1, 2, -2, ...

θ = π/6 + kπ or 5π/6 + kπ

Solutions in the interval [0, 2π] are π/6, 5π/6, 7π/6, 11π/6

Answer 2

2 cos 2θ - 1 = 0

cos 2θ = 0.5

2θ = 60°