Question 627346
{{{4sec^2(x) + 9cosec^2(x)}}}
= {{{(2sec(x) - 3cosec(x))^2 + 12sec(x)cosec(x)}}}


The minimum value of the expression will be obtained when the square term will be zero.
To satisfy that {{{2sec(x) = 3cosec(x)}}}. Thus, the expression reduces to 
{{{8sec^2(x)}}}


This will be minimum when {{{sec^2(x)}}} will be minimum which is 1.

Hence, the minimum value of the given expression is 8.