1@manipal singh.....can u show the solution[7]
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
106the 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
1@ 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???
1nice question Grandmaster
this concept is very helpful in many places
11Write 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.