Question 981328
Foiling them out, one gets f(x)=1-sec^2x



1-(1/cos^2x)=putting it over a common denominator
[cos^2x-1]/cos^2x;  sin^2 x=(1-cos^2x);; sin^2x+cos^2x=1
Therefore, this is - (sin^2 x)(/cos^2 x)= - tan^2 x

Identity is tan^2x+1=sec^2 x
tan^2x=sec^2x-1
-tan^2x=1-sec^2x