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

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Answer 1 · 2018-03-16T03:04:43

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

${cos}^{4} x - 1 = 0$ $cos^4x-1=0$

${cos}^{4} x = 1$ $cos^4x=1$

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

$cos x = \pm \sqrt[4]{1}$ $cosx= +-root(4)(1)$
$cos x = \pm 1$ $cosx= +-1$

$x = 0 and π$ $x= 0 and pi$

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