# Limit problem

## Homework Statement

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

## Homework Equations

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

## The Attempt at a Solution

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I don't know how to convert it to the form of tan (a-b) since there are some extras in the denominator

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Math_QED
Homework Helper
2019 Award
Use distributivity in the denominator and then factor it .

robphy
Homework Helper
Gold Member
Looking only at the denominator, can you write it in another way?

Use distributivity in the denominator and then factor it .
Looking only at the denominator, can you write it in another way?
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!

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