How do I find all solutions for the following equation? 2cos(2Θ) + 1 = 0

Answer 1

2cos(2θ) = 1 So, 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

Answer 2

Convert cos 2θ to either 2 cos² θ - 1 or 1 - 2 sin² θ, then solve by factoring.