Question

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

Answer 1

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

Explanation:

`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`