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Math Help - Express in terms of cosx raised to first power.

  1. #1
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    Express in terms of cosx raised to first power.

    Express cos^2 x sin^2 x in terms of cos x raised to the first power.

    Here is my first attempt at this. I'd like for someone to look over my steps and help me make sure I did this right.

    Using double angle formulas for lowering powers:

    (cos^2x)(sin^2x) = ((1+cos2x)/2) ((1-cos2x)/2)

    = (1 - cos2x + cos2x - cos^2(2x))/4

    = (1 - cos^2(2x))/4

    = (1/4) (1 - cos^2(2x))

    = (1/4) - (1/4) ((1+cos4x)/2)

    = (1/4) - (1/8) + (1/8) cos4x

    = (1/8) + (1/8) cos4x as final answer.
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  2. #2
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    Re: Express in terms of cosx raised to first power.

    Hey FatimaA.

    Check your signs for the 2nd last statement: you should have 1/4 - 1/8 - 1/8 cos(4x) if the above line is correct.
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  3. #3
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    Re: Express in terms of cosx raised to first power.

    (cos^2x)(sin^2x) = ((1+cos2x)/2) ((1-cos2x)/2)

    = (1 - cos2x + cos2x - cos^2(2x))/4

    = (1 - cos^2(2x))/4

    = (1/4) (1 - cos^2(2x))

    = (1/4) - (1/4) ((1+cos4x)/2)


    = (1/4) - (1/8) - (1/8) cos4x

    = (1/8) - (1/8) cos4x
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  4. #4
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    Re: Express in terms of cosx raised to first power.

    Looking good.
    Thanks from FatimaA
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