Question

How do you simplify the expression `(cos^2x-1)/(2-cos^2x+cosx)`?

Answer 1

`(1-cosx)/(cosx-2)`

Explanation:

Let's change signs in the fraction to have:

`-(cos^2 x-1)/(cos^2 x-cos x-2)`

then let's factor:

`-((cos x-1)(cancel(cos x+1)))/((cosx-2)(cancel(cos x +1)))`

that is

`(1-cosx)/(cosx-2)`