Find the minimum value of | sin x + cos x + tan x + cot x + sec x + csc x | for any real number x.

(In reply to answer by Ady TZIDON)

Let x = 2.65344585151355...etc.:

sin(x) 1/2 (1-sqrt(2)+sqrt(2 sqrt(2)-1))   
cos(x) 1/2 (1-sqrt(2)-sqrt(2 sqrt(2)-1))   
tan(x) 1/2 (-1-sqrt(2)+sqrt(2 sqrt(2)-1))   
cot (x) 1/2 (-1-sqrt(2)-sqrt(2 sqrt(2)-1))   
sec (x) 1/2 (1-sqrt(5+4 sqrt(2)))   
csc(x) 1/2 (1+sqrt(5+4 sqrt(2)))   

After cancelling, the |sum| of these is 2*2^(1/2)-1, which is slightly less than 2.

Edited on March 2, 2014, 3:04 pm

Posted by broll on 2014-03-02 15:00:51