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Math Help - Simplifying an equation

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    12

    Simplifying an equation

    Can anyone shed light on how the following simplification was achieved?

    I had: 4a^2 w^2 (coswt + cos2wt)^2 + 4a^2 w^2 (sin2wt - sinwt)^2

    Which became:

    8a^2 w^2 (1 + cos3wt)

    I expect there is a trig identity required but my mind is blank, help!
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  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Re: Simplifying an equation

    To simplify things, look at (\cos(2\theta) + \cos(\theta))^2 + (\sin(2\theta) - \sin(\theta))^2
    = \cos^2(2\theta) +2\cos(2\theta)\cos(\theta) + \cos^2(\theta) + \sin^2(2\theta) -2\sin(2\theta)\sin(\theta)  +\sin^2(\theta)

    =2 + 2(\cos(2\theta)\cos(\theta)-\sin(2\theta)\sin(\theta))

    =2 + 2\cos(2\theta+\theta)
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  3. #3
    Newbie
    Joined
    May 2011
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    Re: Simplifying an equation

    Got it, thank you very much.
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