Question

How do you solve `cos^3 (x) = cos (x)` from 0 to 2pi?

Answer 1

x= 0, `pi/2, pi, (3pi)/2, 2pi`

Explanation:

Rearranging the terms, the given equation is:

`cos^3 x -cos x=0`
`cos x(coa^2 x -1)=0`
`- cos x sin^2 x=0`

This gives cos x=0 or sin^2 x=0

cos x=0 would have x= `pi/2, (3pi)/2`

sin x=0 would have x= 0, `pi, 2pi`