Question

How do you simplify `(cos^2x-4)/(cosx-2)`?

Answer 1

`{cos^2 x - 4}/{cos x - 2} = cos x + 2`

Explanation:

Just use the identity:

`a^2 - b^2 = (a+b)(a-b)`.

Then, we have:

`{cos^2 x - 4}/{cos x - 2} = {(cos x + 2) (cos x - 2)}/{cos x - 2} = cos x + 2`

Answer 2

`cosx+2`

Explanation:

Factorise the numerator as a `color(blue)"difference of squares"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"here "a=cosx" and "b=2`

`rArrcos^2x-4=(cosx-2)(cosx+2)`

`rArr((cancel(cosx-2))(cosx+2))/cancel(cosx-2)`

`=cosx+2`