How do you solve $cos^3x=cosx$ ?

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Answer 1 · 2016-10-06T08:42:33

$x = k pi/2, k = 0,pm1,pm2,cdots$

$cos^3x=cosx$ or
$(cos^2x-1)cos x = -sin^2x cos x = 0$

So we need the $x$ such that make

$cos x = 0$ or $sin x = 0$ or

$cos x = 0 -> x = pi/2+2kpi, k = 0,pm1,pm2,cdots$
$sin x = 0 -> x = pi+2kp, k=0,pm1,pm2,cdots$

or $x = k pi/2, k = 0,pm1,pm2,cdots$

How do you solve cos^3x=cosxcos^3x=cosx?