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

Agnishom
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From: The Complex Plane
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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: 6,092

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: The Complex Plane
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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
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Registered: 2010-06-20
Posts: 6,092

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: 6,092

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: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
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Registered: 2010-06-20
Posts: 6,092

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: The Complex Plane
Registered: 2011-01-29
Posts: 14,191
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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'
'Humanity is still kept intact. It remains within.' -Alokananda

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