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Limit proof of trigonometric function

  1. Jun 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that limh→0[(cos(h-1))/h]=0.

    2. Relevant equations

    Half angle formula
    From an example:

    limh→0[(cos(h-1))/h] = limh→0[-(2sin2(h/2))/h]

    They state that they use the half-angle formula in the following way:

    cosh= 1-2sin2(h/2)

    I'm not really sure how they are getting this from the half angle formula. Any pointer in the correct direction would be greatly appreciated. Thank you, in advance.
     
  2. jcsd
  3. Jun 17, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    Well known identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

    Write cos(h) = cos(h/2 + h/2) and use the identity above along with cos2θ + sin2θ = 1
     
  4. Jun 18, 2012 #3
    Thank you, very much! Somehow I didn't notice to split cos(h) into cos(h/2 + h/2).
     
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