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Homework Help: WHat trig ID is this?

  1. Dec 12, 2007 #1
    I was wondering how my book got from

    8.cos^(2)(x)

    to 4(1+ cos(2x))

    What trig ID is this???

    thank you.
     
  2. jcsd
  3. Dec 12, 2007 #2

    dynamicsolo

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    The identity for (cos x)^2 is constructed from the double-angle formula for cosine,

    cos(2x) = (cos x)^2 - (sin x)^2,

    together with the "Pythagorean Identity",

    (cos x)^2 + (sin x)^2 = 1 .
     
  4. Dec 12, 2007 #3
    But, how did it become 4(1+ cos(2x))?
     
  5. Dec 12, 2007 #4

    dynamicsolo

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    cos(2x) = (cos x)^2 - (sin x)^2 ;

    cos(2x) = (cos x)^2 - [ 1 - (cos x)^2 ] = 2·[ (cos x)^2 ] - 1 ;

    (cos x)^2 = (1/2) · [ 1 + cos(2x) ]

    This is a good derivation to keep in mind for finding (cos x)^2 and (sin x)^2 ; it is the "trick" used when we need to integrate those functions...
     
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