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Derive average rate of change formula of cos

  1. Apr 22, 2013 #1
    Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function:

    (cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h)

    cos(x+h) = cosxcosh - sinxsinh
    subtitute this to (cos(x+h) - cos x)/h we get
    (cos(x+h) - cos x)/h = (cosxcosh - sinxsinh -cosx)/h
    then I know it must go down to =(cosx(cosh - 1) - sinxsinh)/h
    but how does cosxcosh - cosx simpify to cosx(cosh-1)
    sorry my really basic skills are poor
    Thank you a ton!
  2. jcsd
  3. Apr 22, 2013 #2


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    Factor cos(x) from {[cos(x)*cos(h) - cos(x)] - sin(x)*sin(h)}
  4. Apr 23, 2013 #3


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    Well, what do you get if you multiply out cos(x)(cos(h)-1)?
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