What values for θ

Question

(0≤θ≤2π)
satisfy the equation?

4cosθ+1=2cosθ

Answer 1

To solve this equation, we can first move all terms to one side to set it equal to zero.

4cosθ + 1 = 2cosθ
4cosθ - 2cosθ + 1 = 0
2cosθ + 1 = 0

Now, we can simplify the equation by factoring out a 2cosθ:

2cosθ(2 + 1) = 0
2cosθ(3) = 0
cosθ = 0

Now, we need to find the values of θ (0≤θ≤2π) where cosθ = 0.

We know that cosθ = 0 when θ = π/2 and θ = 3π/2.

Therefore, the values of θ that satisfy the equation are θ = π/2 and θ = 3π/2.