show that 8cos^4 x−8cos^2 x+1=cos4x.


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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

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