Cosine sequence

[psyclones]

Hi, I've been pulling my hair out trying to solve this. If we treat it as a series similar to proof by induction it can be simplified. Am I on the right track. But the LHS doesn't appear to factorize and reduce in any easy way!

2017-10-24.pdf

Edited March 13, 2018 by psyclones
attached doc

[Country Boy]

  One error is that taking n= k+ 1 in cos(2nx) gives cos(2(k+ 1)x)= cos((2k+ 2)x), not cos((2k+1)x) as you have.