Average and minimum Values of $|\sin x+ \cos x + \tan x + \cot x +\sec x +\csc x|$, $\forall x \in \mathbb{R}$

Question

A problem was asked at Putnam Competition in 2003 (Problem 3), about finding the minimum Value of $|\sin x+ \cos x + \tan x + \cot x +\sec x +\csc x|$ where $x$ is Real.

the question paper and solutions.

I was thinking if there was any other simpler way to solve this problem. What strategy one should follow to determine the average value of above function?

Answer 1

Please have a look at this: http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2325342&sid=03b52017fa0ef5480a4573048ae117c1#p2325342