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Math Help - verifying

  1. #1
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    verifying

    Can somebody help me verify this?
    -2cos^2xtan(-x)=sin2x
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by unmcintosh View Post
    Can somebody help me verify this?
    -2cos^2xtan(-x)=sin2x
    knowing \tan(-x)=-tan(x)=\frac{sin(x)}{\cos(x)}

    we multiply by cos²(x) to get

    -\sin(x)\cos(x)

    and then dont forget that negative two

    2\sin(x)\cos(x)=\sin(2x)

    QED
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  3. #3
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    Question

    when you multiply by cos^2x, how do you get -sinxcosx?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by unmcintosh View Post
    when you multiply by cos^2x, how do you get -sinxcosx?
    \cos^2(x)\cdot\tan(-x)=\cos^2(x)\cdot\frac{-\sin(x)}{\cos(x)}=-\sin(x)\cos(x)
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