Question

Sec Square X + cos square x can never be less than 2

Answer 1

a + 1/a >= 2. you can check this taking any number;

sec2 x + cos2 x
= sec2 x + 1/sec2 x
= (sec x + 1/sec x)2 - 2
>= 2^2 - 2
>= 2

Answer 2

we know , 
  for all positive real numbers ,
     AM ≥ GM
  
now here two term sec²x and cos²x  and we know both are positive ,
   so, we can use above conccept ,

(sec²x + cos²x)/2 ≥ √(sec²x.cos²x)
(sec²x + cos²x) ≥ 2 .1      [ sec²x.cos²x =1 ]
(sec²x + cos²x ) ≥ 2

    hence sum of sec²x and cos²x is always greater then 2 .