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Trig Identity

  1. May 10, 2007 #1
    The question is "Verify that each equation is an identity."

    tan 8k - tan 8k tan^2 4k = 2 tan 4k

    The first thing I tried was to factor out the tangents.

    tan 8k (1 - tan^2 4k)

    then if I'm doing this correctly

    tan 8k (1 - tan 2k) (1 + tan 2k)

    But from here I'm stuck, that is if I'm on the right track.
  2. jcsd
  3. May 10, 2007 #2
    "tan 8k (1 - tan^2 4k)"

    From here use the double-angle formula.
  4. May 10, 2007 #3
    tan 8k (1 - tan 4k) (1 + tan 4k), this is ok,although you did not need to factorize (1-tan^24k)at all.
    now notice that we can write down tan8k=tan2*4k=2tan4k/(1-tan^2 4k), after substitution look what can be canceled out.
    I am assuming that you already know why
    tan2*4k=2tan4k/(1-tan^2 4k), is so, right??

    Edit: like neutrino said, i just elaborated it a little bit more
    Last edited: May 10, 2007
  5. May 10, 2007 #4
    It is not.
  6. May 10, 2007 #5
    Yeah, sorry by mistake, because i just copied this from the op and did not acyally look at it.!!!!
    What i meant was (1-tan4k)(1+tan4k).

  7. May 10, 2007 #6


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    It might also be a good idea not to lose track of the right side of the equation!
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