Thanks, but it is 27/8
In a triangle ABC , find the least value of,
cot A/2 * cot B/2 * cot C/2 * cos A/2 * cos B/2 * cos C/2
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8 Answers
Asish Mahapatra
·2009-09-20 07:25:26
the value can be simplified as
(s(s-a)s(s-b)s(s-c)s(s-a)s(s-b)s(s-c)(s-b)(s-c)(s-a)(s-c)(s-a)(s-b)bccaab)1/2
= s3/abc
Now can you solve?
it will be min when a=b=c
So, s = 3a/2
hence the min value is 27/8
Grandmaster
·2009-09-21 03:29:35
@ asis how do u get that
it will be min when a=b=c ...........thing.....using some basic funda or a symmetry solution or multi variable calculus???
Philip Calvert
·2009-09-21 03:33:20
nice question Grandmaster
this concept is very helpful in many places
Devil
·2009-09-21 07:34:05
Write S=\frac{a+b+c}{2}
So \frac{s^3}{abc}=\frac{(a+b+c)^3}{8abc}
Whose min occurs at a=b=c by A.M-G.M.