solve

Question

2cos(2θ) + 1 = 0

Answer 1

The trigonometric equation 2 cos(2θ) + 1 = 0

2 cos(2θ) = - 1

cos(2θ) = - 1/2

2θ = cos^-1(-1/2)

2θ = cos^-1(cos 2π/3)

 2θ = 2π/3

θ = π/3

cos(θ) = cos(π/3)

The general solution of cos(x) = cos(α) is x = 2nπ ± α, where n is an integer.

The solutions are θ = 2nπ ± π/3.