Question

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

Answer 1

`frac{4}{3-cos(2x)}+1`

Explanation:

`frac{cos^2(x)-4}{cos^2(x)-2}=frac{2+[2-cos^2(x)]}{2-cos^2(x)}`

`=frac{2}{2-cos^2(x)}+1`

`=frac{4}{4-2cos^2(x)}+1`

`=frac{4}{3-cos(2x)}+1`,

from the double angle identity `cos(2theta)-=2cos^2(theta)-1`.