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#1 2009-08-15 18:40:09

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

Trigonometry Proofs

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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#2 2009-08-15 19:56:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,795

Re: Trigonometry Proofs

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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#3 2009-08-15 19:57:16

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

Re: Trigonometry Proofs

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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#4 2009-08-15 20:04:50

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

Re: Trigonometry Proofs

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

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#5 2009-08-15 20:24:00

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

Re: Trigonometry Proofs

hey i got ans for 4th ques
big_smiletonguemadrollwave;):)
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.wave wave waveroflolroflolroflolupupup:P:P:

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#6 2009-08-16 10:25:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,795

Re: Trigonometry Proofs

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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#7 2009-08-16 12:50:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,795

Re: Trigonometry Proofs

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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#8 2009-08-21 12:01:47

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

Re: Trigonometry Proofs

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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#9 2009-08-21 14:40:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,795

Re: Trigonometry Proofs

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)


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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#10 2009-08-21 19:45:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,795

Re: Trigonometry Proofs

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)


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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