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Composition of trigonometric functions, mean value theorem

  1. Jan 3, 2010 #1
    1. The problem statement, all variables and given/known data

    how to show using MVT that cos(cos x) is a contraction.

    2. Relevant equations

    | d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1

    3. The attempt at a solution

    Using that relation, the original problem is easily solved. My question is, how do we know:

    | sin(cos x) sin(x) | < sin 1 ?

  2. jcsd
  3. Jan 3, 2010 #2


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    Homework Helper

    -1<=cos(x)<=1. What does that make the range of values for sin(cos(x))?
  4. Jan 3, 2010 #3
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