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Thread: Prove Cos3x=4(cos^3)x-3cosx

  1. #1
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    Prove Cos3x=4(cos^3)x-3cosx

    Please help me out with this question


    Use the expansion of cos(A+B) to show that
    Cos3x=4(cos^3)x-3cosx


    This is what i did:
    Cos 3x = (cos^2)x-(sin^2)x
    = (3cos^2)x-1


    I think i am doing something wrong..
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Well, you actually did something wrong...

    Use the expansion of cos(A+B) as you were told.

    \cos(A+B) = \cos A\cos B - \sin A\sin B

    Now, you have cos(3x), make it cos(2x + x) and use the expansion. What do you get?
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  3. #3
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    Quote Originally Posted by Unknown008 View Post
    Well, you actually did something wrong...

    Use the expansion of cos(A+B) as you were told.

    \cos(A+B) = \cos A\cos B - \sin A\sin B


    Now, you have cos(3x), make it cos(2x + x) and use the expansion. What do you get?
    Don't you have to use additon formulae?
    Can you split cos3x?
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  4. #4
    MHF Contributor Unknown008's Avatar
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    I'm sorry, what do you mean by addition formulae?
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  5. #5
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    Quote Originally Posted by Unknown008 View Post
    I'm sorry, what do you mean by addition formulae?
    Addition formulae says that:

    cos(A+b) = cosAcosB-sinAsinB
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Um... is that not what I told you to use?
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  7. #7
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    Quote Originally Posted by Unknown008 View Post
    Um... is that not what I told you to use?
    But, it doesn’t prove that Cos3x=4(cos^3)x-3cosx

    it gives me:
    cos2XcosX-sin2XsinX
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  8. #8
    MHF Contributor Unknown008's Avatar
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    Yes, but how about using it for the time being to see where it leads us?
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  9. #9
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    Quote Originally Posted by mike789 View Post
    But, it doesn’t prove that Cos3x=4(cos^3)x-3cosx

    it gives me:
    cos2XcosX-sin2XsinX
    And, in turn, \cos(2x) = \cos(x+x)
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