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Double-Angle Simplification

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data
    I've been having problems with a lot of identity problems lately, but I've found that I'm especially having issues with problems like this one;
    Verify the identity,

    1/2 Sin (4x) = 2SinxCosx-4Sin3xCosx


    2. Relevant equations
    My professor told me you use Sin(A-B)=SinACosB-CosASinB

    3. The attempt at a solution
    The best I could do was

    1/2 Sin4x=2SinxCox-4Sin3xCos

    1/2Sin4x=2(SinxCosx-2sin3)

    1/2Sin4x=2Sin(x-4x)=-2Sin(3x)

    I know that this is a horrible attempt at solving, but some help would be greatly appreciated.
     
  2. jcsd
  3. Oct 13, 2012 #2

    CAF123

    User Avatar
    Gold Member

    Start with the LHS and write [itex] \frac{1}{2} \sin(4x)\,\,\text{as}\,\, \frac{1}{2} \sin(2x +2x) [/itex] and expand using the addition formula as your professor suggested.
     
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