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    Hi guys!

    Okay I can't do this question, and have spent the last 2 hours on it:/

    1a) By first expressing Cos4x in terms of Cos2x, show that Cos4x=8cos^4 - 8 cos^2 +1

    And hence show that 8 Cos^4x= Cos4x + 4Cos2x +3.

    I don't know where to start tbh!
    I tried using Cos(2x+2x) to get Cos2x.Cos2x - Sin2x.Sin2x
    Therefore I get Cos4x- Sin4x... now I have no idea what do

    Help guys please!
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    \cos 2x \cos 2x \equiv \cos^2 2x \not\equiv \cos 4x

    But you've got the right idea. Use Pythagoras to get everything in terms of cos:

     \cos 4x \equiv \cos^2 2x -\sin^2 2x \equiv \cos^2 2x - (1- \cos^2 2x)

    etc.

    :rolleyes:
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    (Original post by J DOT A)
    Hi guys!

    Okay I can't do this question, and have spent the last 2 hours on it:/

    1a) By first expressing Cos4x in terms of Cos2x, show that Cos4x=8cos^4 - 8 cos^2 +1

    And hence show that 8 Cos^4x= Cos4x + 4Cos2x +3.

    I don't know where to start tbh!
    I tried using Cos(2x+2x) to get Cos2x.Cos2x - Sin2x.Sin2x
    Therefore I get Cos4x- Sin4x... now I have no idea what do

    Help guys please!
    The bolded line is a mistake.
    \cos (2x) . \cos (2x) - \sin (2x) . \sin (2x) \equiv \cos ^2(2x) - \sin ^2(2x) \not\equiv \cos (4x) - \sin (4x).

    Can you recall an identity that connects \sin ^2(2x) and \cos ^2(2x)?

    Spoiler:
    Show
    \sin ^2(2x) + \cos ^2(2x) = 1[/latex].


    Then recall the expansion of cos2x and use the identity linking \sin ^2 x and \cos ^2x to get it all in terms of \cos x.

    For the next part, note that:
    \cos (4x)= 8\cos ^4(x) - 8 \cos ^2(x) + 1
    \Leftrightarrow \cos (4x) = 8\cos ^4(x) - 8\cos ^2(x) +4 -3.

    Can you see the expansion of 4cos 2x in there.
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    (Original post by BJack)
     \cos^2 2x \neq \cos 4x
    Are you sure about that, what about x=0?
    You really need to use "equivalent to" signs (\equiv) rather than "equal to". They have a subtle difference in meaning.
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    (Original post by Farhan.Hanif93)
    Are you sure about that, what about x=0?
    You really need to use "equivalent to" signs (\equiv) rather than "equal to". They have a subtle difference in meaning.
    Ahh thank you! I got the answer!
    However, I don't know how to show that 8Cos^4x= Cos4x + 4cos2x +3

    So rearranging you get 8Cos^4x = Cos4x + 8Cos^2x -1

    Now I don't know what to do!
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    (Original post by Farhan.Hanif93)
    Are you sure about that, what about x=0?
    You really need to use "equivalent to" signs (\equiv) rather than "equal to". They have a subtle difference in meaning.
    Not to a chemist! :p:
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    (Original post by BJack)
    Not to a chemist! :p:
    Sounds like a reasonable excuse to me. I'll let you off.
 
 
 
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