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Another problem

  1. Aug 17, 2008 #1
    1. The problem statement, all variables and given/known data

    sin5xcos3x=sin4xcos4x+sinxcosx, solve the identity

    2. Relevant equations

    all the identities and formulas mentioned in my last thread.

    3. The attempt at a solution

    Alright so I thought I could use the product to sum formula on the left side which ended up being 1/2sin10x then I used the sum/difference formula on the right side and got sin5x. Now according to my calculator these are not the same, so where have I gone wrong?
     
  2. jcsd
  3. Aug 17, 2008 #2

    Defennder

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    Homework Helper

    Applying the product to sum formula to the left side is correct. But you don't end up with sin(10x). Where did you get that from?
     
  4. Aug 17, 2008 #3
    alright what i did was this.

    original problem sin5xcos3x=sin4xcos4x+sinxcosx

    Left side sin5xcos3x

    Product to sum formula sinxcosx=1/2[sin(x+y)+sin(x-y)]
    plug in the numbers

    1/2[sin(5x+3x)+sin(5x-3x)]
    simplify
    1/2(sin8x+sin2x)
    simplify
    1/2sin10x

    right side sin4xcos4x+sinxcosx

    sum/difference formula sin(x+y) = sinxcosy + cosxsiny
    plug in the numbers
    oh,never mind that wont work its in the form sinxcosx +sinycosy hmmm.
     
  5. Aug 17, 2008 #4

    dynamicsolo

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    You're more than halfway home. You have on the left side

    This is fine. You can leave the left side now.

    Alas, angles don't add this way...

    Here, don't apply the product-sum identity to the second term (well, you could, but it's overly fussy). What is sin x·cos x equal to (using another identity)? That will get you one of the pieces you're after.

    Do use the product-sum identity to the first term -- now you'll be done...
     
  6. Aug 17, 2008 #5
    Thank you so much!
     
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