Tag Info

New answers tagged

7

This is an example related to limitations of standard symbolic capabilities of Mathematica, there are many similar issues ( usually they come from arbitrary choices of branches of complex functions), see e.g. analogous problems Why does Integrate declare a convergent integral divergent? or Bug in mathematica analytic integration?. Functions like Log and ...


2

How about this? ArcTan[Simplify[TrigExpand[Tan[5 ArcTan[a] + ArcTan[b]]]]] Could save yourself some work! Explanation: The trick here is to understand the identity you mentioned is about Tan, not ArcTan: Tan[x+y] = (Tan[x]+Tan[y])/(1 -Tan[x]Tan[y]). TrigExpand does the above type of expansion for trig functions. Replace x and y with ArcTan[a] and ...


1

How about: 5 ArcTan[a] + ArcTan[b] /. {(m_Integer: 1) ArcTan[a_] + (n_Integer: 1) ArcTan[b_] /; Positive[m] && Positive[n] :> With[{min = Min[m, n]}, (m - min) ArcTan[a] + (n - min) ArcTan[b] + min ArcTan[(a + b)/(1 - ab)]]} (* 4 ArcTan[a] + ArcTan[(a + b)/(1 - ab)] *) Works on positive integral coefficients, which is how I read ...



Top 50 recent answers are included