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Simplification question


I'd like to verify that the following expression is true for a,b real.
It seems to hold numerically.

1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] ==
ArcTanh[Tanh[a] Tanh[b]]

I tried Reduce and combinations of TrigToExp/Simplify with no luck,
any suggestions?


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