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8 August, 19:20

Solve the equation on the interval [0, 2pi)

2 cos^2 (theta/2) - 3 cos theta = 0

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Answers (1)
  1. 8 August, 19:47
    0
    Hello:

    by idetity : 1+cos (2a) = 2cos² (a)

    let : a = θ/2

    1+cos (2 * θ/2) = 2cos² (θ/2)

    1+cos (θ) = 2cos² (θ/2)

    solve : 2 cos^2 (θ/2) - 3 cos (θ) = 0 ... (1)

    (1) : 1+cos (θ) - 3 cos (θ) = 0

    2cos (θ) = 1

    cos (θ) = 1/2

    in : [0, 2π [

    (θ = π/3) or (θ = 5π/3)
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