Summation and product over $k$ with $k$ prime to $n$ sought

Question

I just come to a standstill with the following two formulas.

If $$E_n=\lbrace k\mid 1\le k\le n\ \&\ (k,n)=1\rbrace$$ then I hope for a closed formula $f(n)$ for those

1. $$\sum_{E_n}k$$

2. $$\prod_{E_n}\cos\left(\frac{k\pi}{n}\right)$$

Would be welcome if the Euler totient $\phi$ function would appear in $f(n)$.

Answer 1

For (2) I made a calculation for $n\ge 3$ and get

$$\prod_{E_n}\cos\left(\frac{k\pi}{n}\right)=\frac{\Phi_n(-1)}{2^{\phi(n)}}$$

This formula may be totally wrong at this moment.

I have not the CAS Mathematica available and also not the programming skills to check it by other CAS freely available.