Finding the limit $\lim_{x \to 0} \frac{1-\prod_{i=1}^n\cos^{1/i}{(ix)}}{1-\prod_{i=1}^n \cos(ix)}$

I was wondering how I could evaluate the expression $L$ as given below.$$\begin{equation}L=\lim_{x \to 0} \frac{1-\displaystyle\prod_{i=1}^n\cos^{1/i}{(ix)}}{1-\displaystyle \prod_{i=1}^n \cos(ix)}.\end{equation}$$I don't think either the Maclaurin series or L'Hopital's rule would immediately apply. Is there any form of transformation I can make to this limit? Thank you for the help.