1no subjective thingy is required....:))
If A,B,C are acute positive angles such that A+B+C=Î
and cot A cot B cot C=k,then
a) k≤1/3√3
b) k≥1/3√3
c) k<1/9
d) k>1/3
The ans is a..... but please can ny 1 giv a proper method 4 dis....
-
UP 0 DOWN 0 0 17
17 Answers
1thanx every one....n gr88 mkagenius........think ill now have to work on am gm a bit more...
24it varies from person to person..........I like to use Jenson's more than AM-GM..........
1Jensens th. is not frequently used by students so am gm might be the winner even when saving time is concerned...whats ur opinion?
24Jensons inequality is also needed for JEE dear........it makes the job easier..........
1students preparing for mathematics olympiads need to know that....i m not preparig for that...
sorry cant tell u.
but u may google it out...u really wanna knw......
62Use the convexity concavity argument...
I think that will work... f(a+b/2) and {f(a)+f(b)}/2
1yes that can b easily solved by am gm
tanA +tanB+tanc>=3(tana*tanb*tanc)1/3
and,tana +tanb +tanc=tana*tanb*tanc;
=>(tana*tanb*tanc)2/3>=3;
=>tana*tanb*tanc>=3√3;
=>cota*cotb*cotc<=1/3√3;
hence u got the ans.....
1am bad wen it comes to subjective maths (not all parts but this trigonometry..) am very used to solving probs by putting angles.. bad habit.. but ... [3]
1[2]
check for some values...
limiting case wen A=B=C
and then chcek for a few values whether its dec or inc from dat limiting value..
am sry if it is subjective [2]