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Trigonometric identities.

  1. Aug 12, 2011 #1
    1. The problem statement, all variables and given/known data

    prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta.

    please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 12, 2011 #2

    eumyang

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    Homework Helper

    So you started at the RHS and got to this:
    2cos4 θ - 2cos2 θ + 1.
    You're really close, then. Split the 2cos4 θ and rearrange the terms like so:
    cos4 θ + 1 - 2cos2 θ + cos4 θ
    Factor the part in bold.
     
    Last edited: Aug 12, 2011
  4. Aug 12, 2011 #3
    Amazing idea that i never thought before !! TQ so much eumyang..
     
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