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Thread: Need help with simple trig proof

  1. #1
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    Need help with simple trig proof

    Use the Pythagorean Trig Identity, sin^2θ+cos^2θ=1, to prove that sin^4θ-cos^4θ=1-2cos^2θ.

    With the advice of my teacher, I started by making a chart. One side is "sin^4θ - cos^4θ", and the other is "1 - 2cos^2θ". He said I'm not supposed to plug in any numerical values, but I'm not sure what to do next.
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  2. #2
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    Re: Need help with simple trig proof

    $\sin^4(\theta) - \cos^4(\theta) = $

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

    $\sin^2(\theta)- \cos^2(\theta) = $

    $(1-\cos^2(\theta))-\cos^2(\theta) = $

    $1 - 2\cos^2(\theta)$
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