Question

How do you solve `cos^2x=cosx`?

Answer 1

`x=pi/2+npi, 2pi+n2pi` where n is an integer

Explanation:

We have:

`cos^2x=cosx`

Let's subtract `cosx` from both sides:

`cos^2x-cosx=0`

`cosx(cosx-1)=0`

Which gives us:

`cosx=0, 1`

When `cosx=0`, we get:

`x=pi/2+npi`

When `cosx=1` we get:

`x=2pi+n2pi`

For both solutions, n is an integer.