Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

How does the identity sinx/cosx work?

Ok I understand that sinx/cosx=tanx
and hence sin2x/cos2x=tan2x
but I can't understand how something I came across the other day works with this identity, somehow;

          -2sin(2x)
         ------------- =-tan(x)?
           2+2sin(2x)
I get where the negative is coming from, that's obvious, but I would have thought it would have been something like tan(2x)?

Can someone please explain?:|

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"If your going through hell, keep going."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: How does the identity sinx/cosx work?

I think Identity is wrong. Try

Last edited by Identity (2009-07-05 00:08:10)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How does the identity sinx/cosx work?

Hi glenn101;

Identity is right, that is not an identity.

Did you mean:

Last edited by bobbym (2009-07-06 11:21:50)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: How does the identity sinx/cosx work?

oh sorry, your quite right, cos was supposed to be on the denominator. And so how is it, that this identity works
sin(2x)
------------- = tan(x)?
cos(2x) +1

Last edited by glenn101 (2009-07-08 12:58:05)

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"If your going through hell, keep going."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How does the identity sinx/cosx work?

Hi glenn101;

I can't explain why it works but I can prove that it does:

Now the 1 in the denominator can be replaced by sin(x)^2 + cos(x)^2

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.