Math Is Fun Forum

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Trig - Compound Angles

Prove that

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

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'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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Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Re: Trig - Compound Angles

Proof

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

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'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'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Trig - Compound Angles

hi Agnishom,

Nice solution!    But check line 5 out of 6.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

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Registered: 2011-02-07

Posts: 3,648

Re: Trig - Compound Angles

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Re: Trig - Compound Angles

Fixed it, Bob

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

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'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'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Trig - Compound Angles

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob