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Minimizing Trigo value (Posted on 2014-03-02) Difficulty: 3 of 5
Find the minimum value of | sin x + cos x + tan x + cot x + sec x + csc x | for any real number x.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (2 votes)

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Some Thoughts re: answer | Comment 2 of 7 |
(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

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