Question

How do you solve  cos³ x = cos x ?

Answer 1

x=kπ/2,k=0,±1,±2,⋯

Explanation:

cos³x=cosx or
(cos²x−1)cosx=−sin²xcosx=0

So we need the x such that make

cosx=0 or sinx=0 or

cosx=0→x=π/2+2kπ,k=0,±1,±2,⋯
sinx=0→x=π+2kp,k=0,±1,±2,⋯

or x=kπ/2,k=0,±1,±2,⋯