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Math Help - Proving a Couple of Trig Identities

  1. #1
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    Proving a Couple of Trig Identities

    sin^2x - tan^2x = -sin^2x tan^2x

    I kept working on tan on both sides, but cannot seem to get them to equal.

    also this one

    sin^4x + 2sin^2x.cos^2x + cos^4x = 1

    I went :
    sin^2x.sin^2x + 2sin^2x.cos^2x + cos^2x.cos^2x

    I tried to make middle one sin2x didn't seem to get me anywhere.
    Also tried changing one of the left sin^2x into 1-cos^2x and
    one of the right cos^2x into 1-sin^2x

    but they didn't cancel each other out.
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  2. #2
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    re: Proving a Couple of Trig Identities

    Quote Originally Posted by Dante View Post
    sin^2x - tan^2x = -sin^2x tan^2x

    I kept working on tan on both sides, but cannot seem to get them to equal.

    also this one

    sin^4x + 2sin^2x.cos^2x + cos^4x = 1

    I went :
    sin^2x.sin^2x + 2sin^2x.cos^2x + cos^2x.cos^2x

    I tried to make middle one sin2x didn't seem to get me anywhere.
    Also tried changing one of the left sin^2x into 1-cos^2x and
    one of the right cos^2x into 1-sin^2x

    but they didn't cancel each other out.
    \sin^2{x} - \tan^2{x} =

    \sin^2{x}\left(1 - \frac{1}{\cos^2{x}}\right) =

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

    \sin^2{x}\left(-\tan^2{x}\right) = -\sin^2{x}\tan^2{x}


    \sin^4{x} +2\sin^2{x}\cos^2{x} + \cos^4{x} =

    \left(\sin^2{x} + \cos^2{x}\right)^2 = \, ?
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  3. #3
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    re: Proving a Couple of Trig Identities

    Quote Originally Posted by Dante View Post
    [B]sin^2x - tan^2x = -sin^2x tan^2x[/B
    \sin^2(x)-\tan^2(x)=\frac{\sin^2(x)(\cos^2(x)-1)}{\cos^2(x)}
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  4. #4
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    re: Proving a Couple of Trig Identities

    Quote Originally Posted by skeeter View Post
    \sin^2{x} - \tan^2{x} =

    \sin^2{x}\left(1 - \frac{1}{\cos^2{x}}\right) =

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

    \sin^2{x}\left(-\tan^2{x}\right) = -\sin^2{x}\tan^2{x}


    \sin^4{x} +2\sin^2{x}\cos^2{x} + \cos^4{x} =

    \left(\sin^2{x} + \cos^2{x}\right)^2 = \, ?
    Woah, that is intense ... I some what understand these steps but it's a lot more advanced than the identities which we are currently being taught.

    Is it possible if you can explain to me how you went from



    to



    Thanks
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  5. #5
    Member sbhatnagar's Avatar
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    Lightbulb re: Proving a Couple of Trig Identities

    Quote Originally Posted by Dante View Post
    Is it possible if you can explain to me how you went from



    to



    Thanks
    a^2+b^2+2ab=(a+b)^2
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