Question

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

Answer 1

$cos^{3}$ x = cos x

$cos^{3}$ - cos x =0

(cos x) ($cos^{2}$ -1 )=0

(cos x )(cos x -1)(cos x + 1)=0

When any of these terms are 0, the equation is satisfied

cos x = 0 => x = 90 degree

cos x -1 =0 => cos x = 1 => x = 0 degree

cos x +1=0 => cos x = -1 => x = 180 degree