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

 Method (no overloads)

Summary

A cos(y) + i A sin(y) below the bar, written as the exponential it is:
A e^(i y), and A cos(y) - i A sin(y) as A e^(-i y). Beside a power
of the cosine above the bar that is an exponential times a power of a cosine, which
the closed rules answer at once; as written it is a sum of a cosine and a sine whose
coefficients have no real rotation -- A^2 + (i A)^2 is zero -- and
cos(x)^2/(a cos(x) + i a sin(x))^3 was declined after twelve seconds.

Remarks

The sibling of SolveByWritingAnImaginaryTangentAsAnExponential(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean), which reads
A + i A tan(y); below the bar only, for the same reason.
 With a constant beside the pair, a + b cos(y) + i b sin(y) is a + b e^(i y),
and there the cosine and sine of y elsewhere are written as exponentials too, so
that the whole is rational in e^(i y): Rubi's
(A + B cos(x))/(a + b cos(x) + i b sin(x)) and its kin were declined, a cosine
beside the exponential being nothing the rules for either read. Without the constant the
cosine above the bar stays, beside the exponential the closed rules answer.
https://github.com/asc-community/AngouriMath/issues/718

























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