Crack this if you have got the brains!!!!!! for a +ve interger n find the least positive value of K

Che

Crack this if you have got the brains!!!!!! for a +ve interger n find the least positive value of K such that cos(x1) +cos(x2)+..........cos(xn) is not greater than K given that tan(x1)tan(x2)tan(x3).......tan(xn)=2^(n/2) for and xi belonging to (o,pi/2)......(in terms of n) and x1>>>> 1 is subscript....i could not find symbols so posted like this.... sorry

Deepak Aggarwal

When n = 1, tan x1 = 1.414 and similarly when n=2 tanx1 + tanx2 = 2

which implies tan x2 = 0.586.

from these values of tan cos x1 = 0.577 and cos x2 = 0.862

since x belogs to 0 to pi/2 , thus cosx can have a maximum of value 1.

add cos x1+ cos x2 > 1 which implies the least positive value of k would be 0.577. reply if still not satisfied!

Che

no not satisfied...

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