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Trignometry

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22 Feb 2007 23:53:57 IST

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trigonometrical inequality

None

sir, there was a question :

derive the minimum value of cos A + cos B + cos C in a triangle where A,B,C are it's angles . one of statements of the proof of this question stated that :

sin A/2 + sin B/2 + sin C/2 will be maximun when A = B = C , how ??

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Rajat Barve

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22 Feb 2007 23:58:17 IST

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even i had the same doubt.but as far as i know the proof of this inequality makes use higher engineering mathematics which includes a complicated taylor's theorem series and partial differentiation

vishak p

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23 Feb 2007 00:07:13 IST

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u sure ??

vishak p

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23 Feb 2007 00:16:11 IST

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please help !

goutham harsha (1nkZ)

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23 Feb 2007 03:29:32 IST

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Checkout the one with the sub: NEED DESPERATE HELP

vishak p

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23 Feb 2007 09:13:19 IST

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i think that answer is also incomplete !

Rajat Barve

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23 Feb 2007 09:24:46 IST

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ya i think i am sure.but if u have asked the experts too,lets wait for their response

Divya Alok Gupta

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23 Feb 2007 13:13:01 IST

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Hey vish0001

i posted the NEED DESPERATE HELP ONE and i think the one who answered it gave it perfectly i wud suggest u look at it closely

vishak p

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23 Feb 2007 20:23:26 IST

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i m not satisfied with that answer ! i mean someone asks me to just derive the minimum value for cos A + cos B + cos C in a triangle, then how shall i proceed ?? also, why will sin A/2 + sin B/2 + sin C/2 be maximun when all the angles are equal to each other ??

amaron

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23 Feb 2007 20:39:28 IST

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Hey Vish0001, sin A/2 + sin B/2 + sin C/2 will be minimum,NOT maximum when A=B=C.This is obvious from the proof of AM>GM ,where AM=GM when all entities are equal.

vishak p

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23 Feb 2007 20:45:21 IST

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ok !!!!! sorry dude !! i did not concentrate on that logic, ok, thanks very much !!

vishak p

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23 Feb 2007 20:50:34 IST

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amaron, canu please explain one thing more to me
why AM >= GM in case of +ve numbers only ?? i am a little confused in this ! hope u reply !

vishak p

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23 Feb 2007 20:51:19 IST

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amaron, canu please explain one thing more to me
why AM >= GM in case of +ve numbers only ?? i am a little confused in this ! hope u reply !

vishak p

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23 Feb 2007 20:53:18 IST

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sorry for the double time question, hope u reply !

Asmita Bhattacharya

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23 Feb 2007 20:55:25 IST

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Obviously if u add 2 -ve no. the sum will b a -ve no. whereas their product will b +ve.

So AM<GM in that case.

vishak p

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23 Feb 2007 20:58:26 IST

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i can understand that, but what shall be the case when there are 3 negative numbers ????

vishak p

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23 Feb 2007 21:14:32 IST

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anyone reply !!

vishak p

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23 Feb 2007 21:16:46 IST

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vamula sreenath

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24 Feb 2007 14:41:08 IST

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we know that in a

cosA+cosB+cosC=1+r/R
so,cosA+cosB+cosC>1
so,there cannot exist minimum value
sincewe know that cosA+cosB+cosC=1+r/R sinX >0 in triangle,
A.M >= G.M is applicable & and so maximum is when A.M = G.M & possible for only equilateral triangle ,so, at A=B=C,sinA+sinB+sinC is maximum

Bipin Dubey

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25 Feb 2007 18:16:39 IST

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sin A/2 + sin B/2 + sin C/2 will be minimum.
Applying AM>=GM and it will be minimum when all the entities are equal.

Vish.....when there are 3 negative numbers then its GM will be root of some negative number which is undefined.Hence the inequality is applicable only for positive numbers.

Hope its clear now.

Best Wishes

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