Solving a Trigonometric Limit Problem

[terryds]

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
Please help

 

[member 587159]

Use distributivity in the denominator and then factor it .

 

[robphy]

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

 

[terryds]

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!

 

[member 587159]

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!

Very well!