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Is This A Correct/Sufficient Proof

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Which is greater cos(sin(x)) or sin(cos(x)), determine with proof.

    3. The attempt at a solution

    http://img21.imageshack.us/img21/5193/proof1ii.jpg [Broken]
    http://img109.imageshack.us/img109/8678/proof2w.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 28, 2009 #2


    Staff: Mentor

    Something you asserted early on is not true - that f(g(x)) = g(f(x)). I stopped reading after that.
  4. Nov 28, 2009 #3
    I was doing proof by contradiction. In order to prove f(g(x)) =/= g(f(x)) i started off by letting f(g(x)) = g(f(x)) and working from there.
  5. Nov 28, 2009 #4


    User Avatar
    Homework Helper

    You would have been doing a proof by contradiction if you said you were doing a proof by contradiction. The way you've written it, you're just asserting (without justification) something that is not even true.

    Other than that, it seems reasonable...
  6. Nov 28, 2009 #5


    Staff: Mentor

    If you're doing a proof by contradiction, you don't start with "therefore ..." - You start by assuming the thing you want to contradict.

    Also, in the same line you have "Therefore g(f(x)) = f(g(x)) cos(sin(x))". It looks like you omitted part of what you wanted to say.
  7. Nov 28, 2009 #6


    User Avatar
    Science Advisor

    I assumed that was a typos for "g(f(x))= f(g(x))= cos(sin(x))". But, in any case, if the problem was to determine which was larger, I don't see what a proof by contradiction that they are not equal would accomplish.
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