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

Agnishom
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From: Riemann Sphere
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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'
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#2 2013-08-18 18:55:51

bob bundy
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Registered: 2010-06-20
Posts: 7,016

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.


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
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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.

I had almost forgotten about the stereograms. What did you figure out about it?


'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 2013-08-19 01:42:48

bob bundy
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Registered: 2010-06-20
Posts: 7,016

Re: Trigonometric Identities

cancel and put over common denominator

add and subtract the term

make use of

Bob

stereogram answer on the other thread


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
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Registered: 2010-06-20
Posts: 7,016

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


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: 21,560
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Re: Trigonometric Identities

Sorry for my late reply.

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'
'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 2013-08-19 15:56:33

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,560
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Re: Trigonometric Identities

bob bundy wrote:

add and subtract the term

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

bob bundy
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Registered: 2010-06-20
Posts: 7,016

Re: Trigonometric Identities

All over the denominator like this:

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

Bob


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
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,560
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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'
'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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