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Limit problem

  1. May 16, 2016 #1
    1. The problem statement, all variables and given/known data

    ##\lim_{a\rightarrow b} \frac{tan\ a - tan\ b}{1+(1-\frac{a}{b})\ tan\ a\ tan\ b - \frac{a}{b}}## = ...

    2. Relevant equations

    tan (a - b) = (tan a - tan b)/(1+tan a tan b)

    3. The attempt at a solution

    I don't know how to convert it to the form of tan (a-b) since there are some extras in the denominator
    Please help
  2. jcsd
  3. May 16, 2016 #2


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    Use distributivity in the denominator and then factor it .
  4. May 16, 2016 #3


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    Gold Member

    Looking only at the denominator, can you write it in another way?
  5. May 16, 2016 #4
    Alright, I've just noticed it...

    ##lim_{a->b}\frac{tan\ a - tan\ b}{(1-\frac{a}{b})(1+tan\ a\ tan\ b)} = lim_{a->b}\frac{tan (a-b)}{(\frac{b-a}{b})} = -b##

    Thanks for help!
  6. May 16, 2016 #5


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    Very well!
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