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Math Help - Where am I messing up? (Proof) [cos3x = 4cos^3x-3cosx]

  1. #1
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    Where am I messing up? (Proof) [cos3x = 4cos^3x-3cosx]

    Hi, I am doing a proof and I have it all down but in the last step it seems as though I distributed my negatives incorrectly. However, I cannot seem to find where. Any help would be great! Thanks!

    cos3x = 4cos^3x-3cosx is the proof. So I did:

    cos3x =
    cos (2x + x) =
    cos2xcosx+sin2xsinx =
    cosx (2cos^2x-1) + sinx(2sinxcosx) =
    2cos^3x - cosx + 2sin^2xcosx =
    2cos^3x - cosx + 2(1-cos^2x)cosx =
    2cos^3x - cosx + 2cosx - 2cos^3x

    However, 2cos^3x - cosx + 2cosx - 2cos^3x Does NOT = 4cos^3x-3cosx
    Whereas 2cos^3x - cosx - 2cosx + 2cos^3x would

    Thanks for any help!
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by SMA777 View Post

    cos (2x + x) =
    cos2xcosx+sin2xsinx =
    It's actually a - sign instead +. (Second step.)
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    It's actually a - sign instead +. (Second step.)
    Er... maybe I'm just being dense, but why?

    Oh, I copied my Sum/Difference formula incorrectly! Got it. Thank you!
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