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SolveByWritingAnImaginaryTangentAsAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)

Method (no overloads)

Summary

A + i A tan(z) is A e^(i z)/cos(z), and A + i A cot(z) is
i A e^(-i z)/sin(z) -- exactly, wherever the tangent is defined, since
cos(z) + i sin(z) is e^(i z). A power of one of them below the bar is
then a power of the cosine times an exponential, and beside a polynomial that is a
shape the closed rules answer: (c + d x)^2/(a + i a tan(pe + f x))^2 is a
search past the budget as written and a second once rewritten.

Remarks

The four signs are the four identities: A - i A tan(z) is
A e^(-i z)/cos(z) and A - i A cot(z) is -i A e^(i z)/sin(z).
Rubi's 4.3.10 and 4.4.10, where every such row carries the imaginary unit in the
coefficient and nothing else reads it. The same question, not one of its own: what is
handed on is the integrand in another spelling.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

SolveByWritingAnImaginaryTangentAsAnExponential​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

SolveByWritingAnImaginaryTangentAsAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)