show-that-8cos-4-x-8cos-2-x-1-cos4x-

Question Number 104796 by mathocean1 last updated on 23/Jul/20

s h o w t h a t

8 {c o s}^{4} x - 8 {c o s}^{2} x + 1 = c o s 4 x .

Commented by kaivan.ahmadi last updated on 23/Jul/20

c o s 4 x = 2 {c o s}^{2} 2 x - 1 = 2 {(2 {c o s}^{2} x - 1)}^{2} - 1 =

2 (4 {c o s}^{4} x - 4 {c o s}^{2} x + 1) - 1 =

8 {c o s}^{4} x - 8 {c o s}^{2} x + 1

Commented by mathocean1 last updated on 23/Jul/20

t h a n k y o u s i r .

Answered by a.lgnaoui last updated on 24/Jul/20

8 \cos^{4} x - 8 \cos^{2} x + 1 = 2 {(2 \cos^{2} x - 1)}^{2} - 1 = 2 [\cos^{2} (2 x)] - 1 = \cos 4 x