Let f(x)=sin2(x/2)+cos2(x/2)  and g(x)=sec2x−tan2x.  the two functions are equal over the set

Domain of f =Df=R, ∴  g(x)=1−sin2xcos2x   Domain of g =Dg=R−{x:x=(2n+1)π2,n∈I]          cos2x ≠0  ⇒x ≠2n+1π2,n∈I∴Df∩Dg=Dg                   Since two functions are said to equal if both will have same domain=R−{x:x=(2n+1)π2,n∈I]