P and q are positive real numbers.
Let p = (sinx) 2 p = (cosx) 2 x ≠ 0 and x≠kπ/2(k is an integer).
√( 1+p^2)+√( 1+q^2)
= 1/|sinx|+ 1/|cosx|
& gt=2√[ 1/(|sinx|*|cosx|)]
| sinx | * | cosx | & lt=[(sinx)^2+(cosx)^2]/2= 1/2
so 2√[ 1/(| sinx | * | cosx |)]& gt; =2√2
That is, √ (1+p2)+√ (1+Q2) > = 2 √ 2.