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Help w/ quad angle identity

  1. Jan 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Simplify: cos(4θ)


    2. Relevant equations
    cos(2θ)=2cos^2(θ)-1
    sin(2θ)=2sinθcosθ

    3. The attempt at a solution
    First, I broke it into cos(2θ+2θ). Then I expanded it and got cos(2θ)cos(2θ)-sin(2θ)sin(2θ). I then expanded that and got (4cos^4(θ)-4cos^2(θ)+1)-(4sin^2(θ)+4sin(θ)cos(θ)+cos^2). I was supposed to get 8cos^4(θ)-8cos^2(θ)+1. I see that I'm off but I don't know where I went wrong.
     
  2. jcsd
  3. Jan 11, 2012 #2

    jedishrfu

    Staff: Mentor

    from your work:

    the term (4sin^2(θ)+4sin(θ)cos(θ)+cos^2) isn't right for sin^2(2x) = (2sin(x)cos(x))^2 = 4 sin^2(x)cos^2(x)

    a simpler derivation would be:

    cos(4x) = 2 cos^2(2x) - 1 right?

    next we look at the cos(2x) factor: cos(2x) = 2cos^2(x) -1

    and plug back into the 2cos^2(2x) - 1
     
    Last edited: Jan 11, 2012
  4. Jan 11, 2012 #3
    Oh, thanks for catching my mistake. I think I can figure it out now but I don't see how you got from cos(4x) to 2 cos^2(2x)-1.
     
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