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Math Help - Factoring

  1. #1
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    Factoring

    I am supposed to factor a trig expression.

    the expression is:

    1-2 sin^2x+sin^4x

    Any help is appreciated!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by vrod guy View Post
    I am supposed to factor a trig expression.

    the expression is:

    1-2 sin^2x+sin^4x

    Any help is appreciated!
    note that your expression is a quadratic in \sin^2 x. to see this, let a = \sin^2 x, then your expression is

    1 - 2a + a^2

    now hopefully you can factor that, then just replace a with \sin^2 x when done
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  3. #3
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    Jhevon,
    When I factored, I came up with (1-sin^2x)^2=cos^4x. Is this correct? Vrod guy, I hope I was able to come up with the correct answer for you.
    Last edited by scottsw1; April 19th 2009 at 06:48 AM.
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  4. #4
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    Scott, Are you sure this is correct? Does anyone else agree with Scott?
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  5. #5
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    Not if you were asked to factorise.

    1 - 2a + a^2 = (1 - a)^2

     = (1 - \sin^2{x})^2

     = \left[(1 + \sin{x})(1 - \sin{x})\right]^2.
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