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#1 2014-05-04 03:40:37

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,007
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Trig - Compound Angles

Prove that

tan 8θ - tan 6θ - tan 2θ = (tan 8θ)(tan 6θ)(tan 2θ)


'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 2014-05-04 03:57:28

Agnishom
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From: The Complex Plane
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Re: Trig - Compound Angles

Proof






Last edited by Agnishom (2014-05-04 22:20:19)


'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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#3 2014-05-04 08:19:56

bob bundy
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Registered: 2010-06-20
Posts: 6,315

Re: Trig - Compound Angles

hi Agnishom,

Nice solution!  smile  But check line 5 out of 6.

Bob


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

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#4 2014-05-04 13:25:23

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Re: Trig - Compound Angles

Agnishom wrote:

Prove that

tan 8θ - tan 6θ - tan 2θ = (tan 8θ)(tan 6θ)(tan 2θ)

I haven't looked at your proof, but here's what I would do:

tan8θ - tan6θ - tan2θ
= tan8θ-(tan6θ + tan2θ)
= tan8θ - tan(6θ + 2θ)(1 - tan6θ * tan2θ)
= tan8θ - tan8θ * (1 - tan6θ * tan2θ)
= tan8θ(1 - 1 + tan6θ * tan2θ)
= tan8θ * tan6θ * tan2θ

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#5 2014-05-04 22:20:55

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,007
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Re: Trig - Compound Angles

Fixed it, Bob

Shivam, That is the same thing I've done. Thanks for helping, though.


'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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#6 2014-05-05 01:02:14

bob bundy
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Registered: 2010-06-20
Posts: 6,315

Re: Trig - Compound Angles

smile smile smile

Bob


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

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