Question 1046263
{{{sin^2(x)+cos^2(x)+sec^2(x)+csc^2(x)+tan^2(x)+cot^2(x) = 1+ tan^2(x) +1 +cot^2(x) +1 +tan^2(x) +cot^2(x)}}}

= {{{3+ 2(tan^2(x) + cot^2(x)) = 3+ 2(tan^2(x) + 1/tan^2(x)) }}}.

Whenever {{{alpha > 0}}}, the relation {{{alpha + 1/alpha >= 2 }}} is always true.

===> The minimum of the original expression is 3 + 2*2 = {{{highlight(7)}}}.