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17 October, 12:27

Verify that 1 + cos 2 theta / 2 cos theta = cos theta is an identity

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Answers (2)
  1. 17 October, 16:25
    0
    (1 + cos (2theta)) / 2cos (theta)

    cos (2theta) = 2cos² (theta) - 1

    (1 + 2cos² (theta) - 1) / 2cos (thetal

    2cos² (theta) / 2cos (theta)

    cos (theta)
  2. 17 October, 16:26
    0
    Answer and Step-by-step explanation:

    We want to verify that (1 + cos (2θ)) / 2cos (θ) = cos (θ).

    Let's focus on the left side. Look at cos (2θ). This is an identity, so remember that cos (2θ) = cos²θ - sin²θ. Also, look at the 1. Remember that sin²θ + cos²θ = 1, so plug both of these expressions into our equation:

    (1 + cos (2θ)) / 2cos (θ) = ? cos (θ)

    ((sin²θ + cos²θ) + (cos²θ - sin²θ)) / 2cos (θ) = ? cos (θ)

    2cos²θ / 2cosθ = ? cosθ

    cosθ = cosθ

    Thus, we have proved this is an identity.
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