Specifically, I know that
JacobiCN[EllipticF[I x, 2], 2]==Cosh[x] for complex x (e.g., check with series expansion in x about x=0), but
FullSimplify will neither confirm the identity nor simplify the left side to the right side.
How can I "teach" MMA to simplify the above to
Cosh[x]? There are a number of other Jacobi Elliptic function identities that I would like to "teach" MMA in order to make life easy.
CLARIFICATION: I would like the following to yield
FullSimplify[JacobiCN[EllipticF[I x], 2], 2]
I would like it to do so for any argument, not just x, since I don't know in advance what the argument will be. For example,
FullSimplify[JacobiCN[EllipticF[I y], 2], 2]==Cosh[y] FullSimplify[JacobiCN[EllipticF[I Sin[a]^b, 2], 2]==Cosh[Sin[a]^b]
should both yield True. x,y,a,b, etc. are generally complex numbers.