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**Fla$h****Member**- Registered: 2009-08-15
- Posts: 10

Hi Guys,i hope im posting in the right forum.Here Are A Few Exercises:-

PROVE THE FOLLOWING:-

1)

2)

3)

4)

5)

6)

I got these out of a maths textbook

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Fla$h;

For #1)

Cross multiply and we have.

*Last edited by bobbym (2009-08-15 20:04:19)*

**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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**juriguen****Member**- Registered: 2009-07-05
- Posts: 59

Hi!

I think I got the first one:

1.

Jose

Make everything as simple as possible, but not simpler. -- Albert Einstein

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

Most trig proofs involve converting 'tan' and 'cot' to 'sin' and 'cos', and lots of fractions!

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**yamini****Member**- Registered: 2009-08-10
- Posts: 2

hey i got ans for 4th ques

;):)

sinA-2sincubeA/2coscubeA-cosA

take sinA common in numerator and cos A in denominator

we get

sinA(1-2sinsquareA)/cosA(2cossquareA-1)

cos2A formula is 1-2sinsquareA and 2cossquareA-1

so they both will get cancelled

we get

sinA/cosA=tanA

hence proved. :P:P:

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Fla$h;

Here is another way for #4

*Last edited by bobbym (2009-08-16 10:26:21)*

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Fla$h;

for #6

Expand the LHS.

*Last edited by bobbym (2009-08-16 12:56:20)*

**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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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 120

Hi Fla$h!;

Here's #2...

using

we get

*Last edited by Fruityloop (2009-08-21 12:11:56)*

The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Fla$h;

Problem #3 is not an identity.

It should read:

Now here is the proof for #3:

Now cross multiply:

Now substitute cos²(A) = 1- sin²(A) and clean up:

*Last edited by bobbym (2009-08-21 16:12:07)*

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Fla$h;

For problem #5

Expanding the LHS and remembering that:

We get:

Now using:

and

We get:

Using:

*Last edited by bobbym (2009-08-21 19:48:56)*

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

Combinatorics is Algebra and Algebra is Combinatorics.

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