AngouriMath
SolveAnEvenPowerOfATangentOverAPowerOfOnePlusASecantByCancelling(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
An even power of a tangent over a power of k (1 +- sec(y)) , cancelled where the
power above is at least twice the one below:tan^2 = (sec - 1)(sec + 1) , so
tan(y)^m/(k (1 + sec(y)))^n is tan(y)^(m - 2 n) (sec(y) - 1)^n/k^n , and
overk (1 - sec(y)) it is tan(y)^(m - 2 n) (sec(y) + 1)^n/(-k)^n .
power above is at least twice the one below:
over
Remarks
Rubi's 4.5.1.4 tan(c + d x)^12/(a + a sec(c + d x))^3 ran out of time, and
tan(c + d x)^6 (sec(c + d x) - 1)^3/a^3 is answered in a third of a second.
From the twelfth power only, where the rules after it stop answering in time --
tan^12/(a + a sec) and tan^14/(a + a sec)^3 ran past a minute -- since
below it they answer more shortly:tan^10/(a + a sec)^3 in 507 characters
where cancelled it is 851.
https://github.com/asc-community/AngouriMath/issues/233
From the twelfth power only, where the rules after it stop answering in time --
below it they answer more shortly:
where cancelled it is 851.
https://github.com/asc-community/AngouriMath/issues/233
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