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If sin(B+C-A),sin(C+A-B) and sin(A+B-C)are in A.P.; then cot A,cot B,cot C are in -

(a) GP

(b) HP

(c) AP

(d) None of these.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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M says b. I haven't gotten to the solution analytically yet, though.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

May I see what you did with M to get that?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Sure!

```
FullSimplify[Sin[b + c - a] + Sin[a + b - c] == 2 Sin[a + c - b]]
2 Cos[a] Cos[c] Sin[b] == Cos[b] Sin[a + c]
```

*Last edited by anonimnystefy (2014-07-14 05:02:14)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I do not understand it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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What do you not understand? I just rearranged the result a bit and got the answer.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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They are in AP?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

The cot's are in HP.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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How are you representing the sines in AP is what I meant?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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The same as Nehushtan did.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Okay, I see what you saying.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Now to do it by hand...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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You have the result, now you just have to back engineer the how.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

I think I figured it out. I will post it when I write it out.

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**anonimnystefy****Real Member**- From: The Foundation
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Here's the solution.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Got to get off, will look at it when I get back. You did good.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Expanding gives:

hence in H.P.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Hi bobbym

See you later!

Thanks.

*Last edited by anonimnystefy (2014-07-14 06:29:01)*

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