Let Me Give You More Trouble

Calculus Level 4

\[ \large \lim_{x \to 0} \frac{ 1- \displaystyle \prod_{k=1}^{100} \cos kx}{x^2} = \, ? \]

Bonus: Generalize for \(n\) or \(\displaystyle \lim_{x \to 0} \frac{ 1-\prod_{k=1}^{n} \cos kx}{x^2}\).