# Math Help - minimum value

1. ## minimum value

Find the minimum value of expression:
$|cos a|+|cos b|+|cos c|+|cos(a-b)|+|cos(b-c)|+|cos(c-a)|$
I need some ideas. thank you

2. Originally Posted by ely_en
Find the minimum value of expression:
$|\cos a|+|\cos b|+|\cos c|+|\cos(a-b)|+|\cos(b-c)|+|\cos(c-a)|$
I need some ideas. thank you
The smallest value I can find is 2, attained for example when $(a,b,c) = (-\pi/2,0,\pi/2)$. This looks like a local minimum, but I don't see how to prove that it is a global minimum.