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## #1 2013-08-19 12:49:05

Agnishom
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### Trigonometric Identities

Prove these:

1.

2. If cosec  θ - sin  θ = a3 and sec  θ - cos  θ = b3, Then prove that: a²b²(a² + b²) = 1

Last edited by Agnishom (2013-08-19 14:37:06)

'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'
'The whole person changes, why can't a habit?' -Alokananda

## #2 2013-08-19 16:55:51

bob bundy
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### 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

## #3 2013-08-19 22:39:22

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #4 2013-08-19 23:42:48

bob bundy
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### Re: Trigonometric Identities

cancel and put over common denominator

make use of

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #5 2013-08-20 00:08:33

bob bundy
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### 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

## #6 2013-08-20 13:50:39

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #7 2013-08-20 13:56:33

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #8 2013-08-20 17:16:11

bob bundy
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### 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

## #9 2013-08-20 17:48:19

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda