Question

How to solve `cos^2theta-costheta=0` if `0<x<360`?

I don't understand why the answer is `theta=0, 90, 270, 360` degrees as I only get `theta=0, 360` when I use a cos graph.

Answer 1

`cos^2theta-costheta=0`

`costheta(costheta-1)=0`

`costheta= 0`
`theta=90^@, 270^@`

`costheta=1`
`theta= 0^@, 360 ^@`

What you probably did is-
`cos^2theta=costheta`

`costheta=1`

Can't do that, because you lose solutions, avoid dividing by `sinx`, `cosx` etc.

Take:
`x^2-x=0`

`x^2=x`

`x=1`

But we also know `0` is a solution, so can't divide by `x` in quadratics as well