Question

How do you simplify the expression `(cos^2(x)+cos(x)-20)/(cos^2(x)-16)`?

Answer 1

`(cos^2x+cosx-20)/(cos^2x-16)=1+1/(cosx+4)`

Explanation:

`(cos^2x+cosx-20)/(cos^2x-16)`

= `(cos^2x+5cosx-4cosx-20)/((cosx-4)(cosx+4))`

= `(cosx(cosx+5)-4(cosx+5))/((cosx-4)(cosx+4))`

= `((cosx-4)(cosx+5))/((cosx-4)(cosx+4))`

= `(cosx+5)/(cosx+4)`

= `1+1/(cosx+4)`