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Math Help - factor

  1. #1
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    factor

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

    I believe the answer is cos^4x

    I want to say that 1-2(1+sin^2x)(sin^2x) if I move it around I get

    I do not know where to go next or how it is cos^4x
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  2. #2
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    Double angle formulas may help here
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  3. #3
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    Quote Originally Posted by IDontunderstand View Post
    1-2sin^2x+sin^4x

    I believe the answer is cos^4x

    I want to say that 1-2(1+sin^2x)(sin^2x) if I move it around I get

    I do not know where to go next or how it is cos^4x
    As it says "factor" in your thread title...

    y=sin^2x

    and using sin^2x+cos^2x=1\Rightarrow\ sin^2x=1-cos^2x

    1-2y+y^2=(y-1)(y-1)=\left(sin^2x-1\right)\left(sin^2x-1\right)=\left(1-cos^2x-1\right)\left(1-cos^2x-1\right)

    which leads to the answer.
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  4. #4
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    Hello, IDontunderstand!

    \text{Sinplifyt: }\:1-2\sin^2\!x+\sin^4\!x

    \text{I believe the answer is: }\:\cos^4\!x

    Factor: . 1 - 2\sin^2\!x + \sin^4\!x \;=\;(\underbrace{1 - \sin^2\!x}_{\text{This is }\cos^2\!x})^2 \;=\;(\cos^2\!x)^2 \;=\;\cos^4\!x

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