Let [tex] T_n = \cos(\theta/2)\cos(\theta/4)\cos(\theta/8)...\cos(\theta/2^n)[/tex]
when n tend to infinity
For n is very large
Here is my solution : consider the function . Its zeroes are and for , Thus its zeroes are all , , which are the zeroes of .
Moreover we know must be an entire function because it is a product of entire functions. By the identity theorem for entire functions, we must have for some . If we consider the coefficient of in the series expansion of about , we see that it is equal to , and on the left side as well. Hence we must have and .