Question

2cos^2theta-3costheta+1=0

Answer 1

Explanation:

To answer this question, we can begin by creating factors from this equation:

(2cosθ-1)(cosθ-1)= 0.

Now, we just need to set the factors equivalent to 0 and solve:

2cosθ= 1.

cosθ= 1/2

θ=
`(\pi )/(3)`,
`(5\pi )/(3)`

cosθ= 1

θ= 0, 2
`\pi`.

Answer 2

Answer: Theta (θ) = 2πn, π/3 + 2πn, 5π/3 + 2πn

Explanation:

2cos²(θ) - 3cos(θ) = -1

Let cos(θ) = u

2u² - 3u + 1 = 0

u = 1, u = 1/2

Substitute u with cos(θ) and you have your answer.

I used Symbolab's variable solving calculator for this since I'm lazy :\