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I had the same problem, I don't know the reason why g(x) = f(h(x)) does not work. But this works (Sage 9.2):

g(x) = [*f(h(x))]

and for g, and g(x) you get:

x ↦ (sin(h(x)),cos(h(x)))
(sin(h(x)),cos(h(x)))

Here, we are basically unpacking and then repacking the array!