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28 November, 23:09

1. Derive formulas for the following:

a. sin (2theta)

b. cos (2theta)

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Answers (1)
  1. 28 November, 23:20
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    Sin (2theta) = 2sintheta costheta

    Cos (2theta) = 2cos²theta - 1

    Cos (2theta) = 1 - 2sin²theta

    Step-by-step explanation:

    Sin (2theta) = Sin (theta+theta)

    Sin (theta+theta) = sintheta costheta + costheta sintheta

    Since costheta and sintheta are occurring twice in the addition

    Sin (theta+theta) = 2sintheta costheta

    Cos (2theta) = cos (theta+theta)

    = costheta costheta - sintheta sintheta

    = cos²theta - sin²theta ... 1

    From sin²theta + cos²theta = 1

    Sin²theta = 1 - cos²theta ... 2

    Substituting 2 into 1

    Cos (2theta) = cos²theta - (1 - cos²theta)

    Cos (2theta) = cos²theta - 1 + cos²theta

    Cos (2theta) = 2cos²theta - 1

    Cos (2theta) = 1 - 2sin²theta
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