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Question: How to convert this answer to this format?

Question:How to convert this answer to this format?

minhthien2016 385 Maple
recurrence sequence
September 30 2018
2

I want to find general formulas of the sequence satifies:
f(1) = 1, f(n+1) = 1/2*(f(n)+9/f(n))
I tried 
restart;
rsolve({f(1) = 1, f(n+1) = 1/2*(f(n)+9/f(n))}, {f})
I got the answer
3*coth((1/2)*arccoth(1/3)*2^n)

How to get the form (-3*2^(2^(-1+n))+3*(-1)^(1+2^(-1+n)))/(-2^(2^(-1+n))+1)?
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