# Limit problem

1. May 16, 2016

### terryds

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

2. May 16, 2016

### Math_QED

Use distributivity in the denominator and then factor it .

3. May 16, 2016

### robphy

Looking only at the denominator, can you write it in another way?

4. May 16, 2016

### terryds

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!

5. May 16, 2016

Very well!