The discussion revolves around evaluating a limit involving trigonometric functions, specifically the limit of the difference of tangent functions as one variable approaches another. The problem is situated within the context of trigonometric limits and their properties.
Some participants have offered guidance on manipulating the expression, while others have noted their realizations about the limit's structure. The discussion reflects a collaborative effort to clarify the problem without reaching a definitive conclusion.
There appears to be some confusion regarding the additional terms in the denominator and how they affect the limit's evaluation. Participants are navigating the constraints of the problem as they work through their reasoning.
Math_QED said:Use distributivity in the denominator and then factor it .
robphy said:Looking only at the denominator, can you write it in another way?
terryds said: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!