AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug ~~Donate~~ Contacts

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

Method (no overloads)

Summary

A product of two tangents, cotangents, secants or cosecants of linear arguments whose
difference or sum is a constant, written as the functions of each apart: with
d = A - B, tan(A) tan(B) = cot(d) (tan(A) - tan(B)) - 1.

Remarks

The addition formulas, read for the product: for a constant d = A - B,
tan(A) tan(B) = cot(d) (tan(A) - tan(B)) - 1,
cot(A) cot(B) = cot(d) (cot(B) - cot(A)) - 1,
sec(A) sec(B) = csc(d) (tan(A) - tan(B)) and
csc(A) csc(B) = csc(d) (cot(B) - cot(A)); for a constant s = A + B,
tan(A) tan(B) = 1 - cot(s) (tan(A) + tan(B)),
cot(A) cot(B) = 1 + cot(s) (cot(A) + cot(B)),
sec(A) sec(B) = csc(s) (tan(A) + tan(B)) and
csc(A) csc(B) = csc(s) (cot(A) + cot(B)). Each holds wherever both sides are
defined, for d or s not a multiple of pi, which a symbolic one is
taken not to be, as everywhere in this integrator. Rubi's 4.7.7 has
tan(a + b x) tan(c + b x) and the rest, and nothing read two arguments.
The same question in another spelling, so asked as it. A constant times the product
only, and the two functions of one kind.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

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

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