Solve $cos^4x-1=0$ for all values of x?

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Answer 1 · 2018-03-16T03:04:43

General solution
$x= 0+2pin$
$x= pi+2pin$
$n$ is an element of all integers

$cos^4x-1=0$

$cos^4x=1$

Fourth root both sides (remember for all implemented even roots, the value can be positive or negative):

$cosx= +-root(4)(1)$
$cosx= +-1$

$x= 0 and pi$

General solution
$x= 0+2pin$
$x= pi+2pin$
$n$ is an element of all integers