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

here the least value is obtained when triangle is eqilateral triangle:

A=B=C=60^o

cot A/2 * cot B/2 * cot C/2 * cos A/2 * cos B/2 * cos C/2 =  (cot 30 * cos30 )³ 

= 3/2

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Ramesh  
IIT Kgp - 05 batch

Sir, why is the triangle considered to be equilateral, is there any reason behind that, or how can conclude such things sir....plz help me??

since the least value, which we want to find - applies for all triangles ( be a scalene,obtuse,right angled); the simplest case can be an equilateral triangle.

I suggest when ever, if an objective question comes on propoeties of triangles, take the case of an equilateral triangle - and u shld find the answer in one of options

Sir isn't the final answer (3/2)^3