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## #1 2013-08-18 14:49:05

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
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### Trigonometric Identities

Prove these:

1.

2. If cosec  θ - sin  θ = a[sup]3[/sup] and sec  θ - cos  θ = b[sup]3[/sup], Then prove that: a²b²(a² + b²) = 1

Last edited by Agnishom (2013-08-18 16:37:06)

'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'
I'm not crazy, my mother had me tested.

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## #2 2013-08-18 18:55:51

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Trigonometric Identities

hi Agnishom,

Starting with

That looks like a good way to start with those denominators.  Then put everything in terms of sin and cos in order to simplify.

The second identity looks somewhat tougher.  I'll come back if I make progress.

Bob

ps.  I've made some progress with stereograms.

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 2013-08-19 00:39:22

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
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### Re: Trigonometric Identities

Thanks but I know these Identities. Yet, I am not being able to solve that at all. Please help me out.

'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'
I'm not crazy, my mother had me tested.

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## #4 2013-08-19 01:42:48

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Trigonometric Identities

cancel and put over common denominator

make use of

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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## #5 2013-08-19 02:08:33

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Trigonometric Identities

I may have gone 'round the houses' to do the second, but it works.  In other words, some steps may be eliminated I think.

exercise for you: do a similar thing with b^3

evaluate a/b and b/a and substitute all into (1)

everything cancels leaving just a 1

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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## #6 2013-08-19 15:50:39

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
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### Re: Trigonometric Identities

I will do these as soon as possible

'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'
I'm not crazy, my mother had me tested.

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## #7 2013-08-19 15:56:33

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
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### Re: Trigonometric Identities

bob bundy wrote:

Like this?

'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'
I'm not crazy, my mother had me tested.

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## #8 2013-08-19 19:16:11

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Trigonometric Identities

All over the denominator like this:

Then put the first three into a 'perfect square'.

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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## #9 2013-08-19 19:48:19

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
Website

### Re: Trigonometric Identities

:d

'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'
I'm not crazy, my mother had me tested.

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