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**mickeen****Member**- Registered: 2009-04-18
- Posts: 10

(a) Express Sin2A + Sin2B as a product in Sine and Cosine.

(b) If A + B + C = 180 degrees,

show that Sin (A + B) = Sin C

(c) Hence show that Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

Note: Cos(A + B) = - CosC

Can anyone plese help me on the last part of this question which has bothered me for some time now.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,491

Hi mickeen;

a) First thing that comes to mind is:

b) If A + B + C = 180 then A + B = 180 - C and

sin( 180 - c ) = sin(180° )cos(c) - cos(180° )sin(c)

= sin(c)

For c)

(c) Hence show that Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

What does the underscore mean?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

(a) Express Sin2A + Sin2B as a product in Sine and Cosine.

*Last edited by ZHero (2010-05-10 20:08:26)*

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,491

Hi mickeen;

For C)

Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

I going to assume you meant:

remember sin(C) = sin(A+B)

See the result I gave you in post #6, Use it right here.

Done!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

(b) If A + B + C = 180 degrees,

show that Sin (A + B) = Sin C

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,491

Hi mickeen;

For a) this came to me while doing c)

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

The sum to product formulas:

Just say u = 2A and v = 2B

And you get:

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mickeen****Member**- Registered: 2009-04-18
- Posts: 10

Thanks a million for this. I have printed it off and will try to digest it over a bowl of soup and a glass of wine later tonight!

mickeen

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,491

Hi mickeen;

Enjoyed working on c), thanks for posting it. Save me some soup.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**mickeen****Member**- Registered: 2009-04-18
- Posts: 10

Bobby M,

thanks for your help again this time! Dont know what I would do without you! I have it all written out now again (your explanation) and understand it perfectly. Are you any good on Stats? I am OK a while but might have a few questions in June. The soup and the wine was nice. But all gone by the end of the 80 mile cycle yesterday morning! I suppose one cant really share cyber soup! However! Thanks again!

Mickeen

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,491

Hi mickeen;

You mean I got some of that right!!!!! I knew those Tarot cards worked.

Thanks man. I am glad you got it. I can do some stats and I like it. I am unusually good in stats, getting half of the questions right, provided it is a 2 choice per question test. I know what you would do without me, better! Bring it in and if I am around I will help. Don't worry about the soup.

Just let me say, thanks for saying those kind things, lately I have been feeling pretty unappreciated by some people.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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