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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'

'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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**bob bundy****Moderator**- Registered: 2010-06-20
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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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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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

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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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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bob bundy wrote:

add and subtract the term

Like this?

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,020

All over the denominator like this:

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

Bob

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:d

'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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