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Math Help - Can you prove this identity?

  1. #1
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    Can you prove this identity?

    cos²x - sin²x = cos2x +sin²x
    Last edited by advancedfunctions2010; April 18th 2010 at 09:19 PM.
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  2. #2
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    Quote Originally Posted by advancedfunctions2010 View Post
    cos²x - sin²x = cos2x +sin²x






    Thanks!
    Are they equal..?

    \cos(2x) = \cos(x+x) = \cos(x)\cos(x) - \sin(x)\sin(x) = \cos^2(x) - \sin^2(x)

    So \cos(2x) + \sin^2(x) = \cos^2(x)...
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  3. #3
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    hm you see I created this identity.. it's a class assignment and we have to see if someone can prove it?

    I started off with cos²x = cos²x

    and from there you're supposed to keep replacing terms with equivalent equations to make it complex.

    Im trying to see if it makes sence and if its possible to prove..
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  4. #4
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    Quote Originally Posted by advancedfunctions2010 View Post
    hm you see I created this identity.. it's a class assignment and we have to see if someone can prove it?

    I started off with cos²x = cos²x

    and from there you're supposed to keep replacing terms with equivalent equations to make it complex.

    Im trying to see if it makes sence and if its possible to prove..
    \cos(2x) + \sin^2(x) = \cos^2(x) - \sin^2(x)

    Set x = \frac{\pi}{2}.

    \cos(\pi) + \sin^2(\pi/2) = -1 + 1 = 0

    But

    \cos^2(\pi/2) - \sin^2(\pi/2) = 0 - 1^2 = -1.

    Not the same thing am afraid.

    Show me how you got it and I'll show you where you went wrong...
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  5. #5
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    Okay so I started with..

    cos²x = cos²x

    1 - sin²x = cos2x + sin²x

    cos2x = 1 - 2sin²x + sin²x

    cos x cos y - sin x sin y = cos2x + sin²x (after here i didn't know how to break down the right side any further)

    cos²x - sin²x = cos2x + sin²x
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  6. #6
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    Quote Originally Posted by advancedfunctions2010 View Post
    1 - sin²x = cos2x + sin²x

    cos2x = 1 - 2sin²x + sin²x
    Are both the left hand sides equal..?

    You have put down...

    \cos(2x) = 1 - \sin^2(x) and also \cos(2x) = 1 - 2\sin^2(x)
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  7. #7
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    I'm not sure haa.. I'll just have to try from the start again..

    thanks for your time though!
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