1-prove-that-n-2-n-inyegr-x-2n-1-x-1-x-1-k-1-n-1-x-2-2cos-kpi-n-x-1-2-find-the-value-of-0-pi-ln-x-2-2xcost-1-dt-

Question Number 40882 by prof Abdo imad last updated on 28/Jul/18

1) p r o v e t h a t \forall n ⩾ 2 (n i n y e g r)

x^{2 n} - 1 = (x - 1) (x + 1) \prod_{k = 1}^{n - 1} (x^{2} - 2 c o s (\frac{k π}{n}) x + 1)

2) f i n d t h e v a l u e o f \int_{0}^{π} l n (x^{2} - 2 x c o s t + 1) d t