Punching that in to WolframAlpha, after rewriting it in terms of hyperbolic cosine, shows that it is indeed an identity: https://www.wolframalpha.com/input/?i=2

Punching that in to WolframAlpha, after rewriting it in terms of hyperbolic cosine, shows that it is indeed an identity: https://www.wolframalpha.com/input/?i=2+Cosh%5BI+%5C%5BPi%5D%2F5%5D https://www.wolframalpha.com/input/?i=2+Cosh%5BI+%5C%5BPi%5D... This occurs via the identity cosh(i x) = cos x, so 2 cosh(i pi/5) = 2 cos (pi/5) and then you go into the usual stuff to evaluate that one.