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!
A trigonometric limit problem is a mathematical problem that involves finding the limiting value of a function as its input approaches a specific value. In the case of trigonometric limit problems, the functions involved are trigonometric functions such as sine, cosine, and tangent.
The strategy for solving a trigonometric limit problem involves using algebraic manipulations, trigonometric identities, and the properties of limits to simplify the expression and evaluate the limit. It is important to also check for any special cases or exceptions that may apply.
Some common trigonometric identities used in solving limit problems include the Pythagorean identities (sin²x + cos²x = 1), the double angle identities (sin2x = 2sinx cosx), and the sum and difference identities (sin(x ± y) = sinx cosy ± cosx siny).
Some common properties of limits used in solving trigonometric limit problems include the sum and difference properties (lim[f(x) ± g(x)] = limf(x) ± limg(x)), the product property (lim[f(x)g(x)] = limf(x) * limg(x)), and the quotient property (lim[f(x)/g(x)] = limf(x)/limg(x)), among others.
Some tips for solving trigonometric limit problems include: identifying and using appropriate trigonometric identities, checking for any special cases or exceptions, breaking down the expression into simpler forms, and practicing a lot of problems to become familiar with the different strategies and techniques used.