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A Trigonometric Identity Probelm

  1. Oct 16, 2008 #1
    [SOLVED] A Trigonometric Identity Probelm

    If I have [tex]sin^2 2x[/tex] would I be able to apply the identity [tex]sin^2x = (1/2)(1-cos2x)[/tex] to get this:

    [tex]sin^2 2x = 2(1/2)(1 - cos^2 x)[/tex]

    Similarly, if I had [tex]sin^2 2x + cos^2 2x[/tex] would I be able to use the identity [tex]sin^2 x + cos^2 x = 1[/tex] to get:

    [tex]sin^2 2x + cos^2 2x = 2[/tex]
    Last edited: Oct 16, 2008
  2. jcsd
  3. Oct 16, 2008 #2

    So in your case theta = 2x
    sin^2(2x)= 1/2(1-cos(4x))
    Last edited: Oct 16, 2008
  4. Oct 16, 2008 #3
    For the second half of your question, sin^2(2x) + cos^2(2x) = 1 (NOT 2)

    Think about it, sin^2(x) + cos^2(x) = 1 for every value of x. So the range for x is (-infinity, +infinity). And of course 2x falls in that range (every real # falls in that range)
    This applies as long as the angles are the same for both sin^2 and cos^2.
  5. Oct 16, 2008 #4
    That explains a lot. I appreciate it, thank you.
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