Thanks for the reply.
I am still hazy about Calculus, but I think that using algebraic identities like (a+b)^2 and (a-b)^2 this can be solved:
sec^2 theta =1/ cos^2 theta. Therefore, cos^2 theta can be taken as 'x' and the equation reduces to x^2 + 1/x^2.
x^2 + 1/x^2 - 2*x*1/x + 2*x*1/x.
(x^2 - 1/x^2)^2 + 2
This way, sec^2 theta + cos^2 theta can never be less than 2. Is this right?