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## #1 2014-04-17 04:17:13

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

### trigonometry

Prove that

Last edited by niharika_kumar (2014-04-17 04:17:45)

friendship is tan 90°.

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## #2 2014-04-17 07:58:11

bob bundy
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Registered: 2010-06-20
Posts: 7,071

### Re: trigonometry

hi Niharika,

No one else is offering a method so here is one that will work.  It's not nice and 'slick' so hopefully someone else will jump in with a simpler method.

If you expand this you'll get the powers of 10 that you need (plus some unhelpful other powers of sin and cos)

But you can write all the cos^2 terms as (1 - sin^2) instead so the unhelpful terms will all become powers of sine.

Do the same for

Now use these formulas to construct the expression

It will come to 1 without all those powers of sine, so they must all cancel out.  Job done!

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2014-04-17 14:22:20

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,764
Website

### Re: trigonometry

Those expressions are factorable...

Last edited by Agnishom (2014-04-17 14:30:42)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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## #4 2014-04-17 14:45:39

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,764
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### Re: trigonometry

Let cos^2 θ = y, sin^2 θ = x

We want to prove that 6(x^5 + y^5) - 15(x^4 + y^4) + 10(x^3 + y^3) - 1 = 0

Now, since cos^2 θ + sin^2 θ = 1, y=1-x

6(x^5 + y^5) = 6(x^5 + (1-x)^5) = 6 - 30 x + 60 x^2 - 60 x^3 + 30 x^4
-15(x^4 + y^4) = -15(x^4 + (1-x)^4) = -15 + 60 x - 90 x^2 + 60 x^3 - 30 x^4
10(x^3 + y^3) = 10(x^3 + (1-x)^3) = 10 - 30 x + 30 x^2

LHS = 6(x^5 + y^5) - 15(x^4 + y^4) + 10(x^3 + y^3) - 1 = 6 - 30 x + 60 x^2 - 60 x^3 + 30 x^4 -15 + 60 x - 90 x^2 + 60 x^3 - 30 x^4 + 10 - 30 x + 30 x^2 - 1 = 0 = RHS

##QED##

Sorry Niharka, we are still needing the binomial theorem. The above is very tedious to d by hand. I used a computer

Last edited by Agnishom (2014-04-17 14:58:45)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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## #5 2014-04-17 16:43:09

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

### Re: trigonometry

let me go and do some problems on binomial theorem first.

friendship is tan 90°.

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## #6 2014-04-19 01:35:34

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,764
Website

### Re: trigonometry

Are you enjoying school?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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## #7 2014-04-19 19:05:11

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

### Re: trigonometry

school hasn't started yet.
It will start only after the results come.

friendship is tan 90°.

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## #8 2014-04-20 05:01:53

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,764
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### Re: trigonometry

We will start this fridday.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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## #9 2014-04-20 15:40:04

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

### Re: trigonometry

great.
you are choosing PCM, right?along with which subject?

friendship is tan 90°.

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## #10 2014-04-20 18:40:31

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,764
Website

### Re: trigonometry

Along with biology.

What about you? Computer Science?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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## #11 2014-04-21 16:07:43

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

### Re: trigonometry

my mother wanted me to take PCMB and become a doctor(as I also scored highest everytime in biology), but i am very sensitive to things , so I dropped the idea.
I was confused between Comp. sc., Economics and P.E., then a comp.sc. student told me that you can learn programming anytime anywhere, so why sit for exams for that as even a small silly error in writing programs can cost loosing good marks.
So now I am confused between Economics and P.E.?
What do you suggest?

friendship is tan 90°.

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