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Old 2019-04-28, 11:54   #1
wildrabbitt
 
Jul 2014

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Default something I think is true but can't prove

Hi,


does anyone know if



sinAcosx - sinxcosA = 0 is true


if and only if sinA = sinx and cosx = cosA are true?



I've tried to prove it. I don't think I can. My mind's not working right anyway.


I thought some help with this might help me straighten my head out a bit.


(it would be appreciated).
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Old 2019-04-28, 12:19   #2
retina
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"The unspeakable one"
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Quote:
Originally Posted by wildrabbitt View Post
Hi,


does anyone know if



sinAcosx - sinxcosA = 0 is true


if and only if sinA = sinx and cosx = cosA are true?



I've tried to prove it. I don't think I can. My mind's not working right anyway.


I thought some help with this might help me straighten my head out a bit.


(it would be appreciated).
Just rename sinA = sinx = E, and cosA = cosx = F

And you get this: EF - EF = 0
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Old 2019-04-28, 12:32   #3
Nick
 
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sin(A)cos(x) - cos(A)sin(x)=sin(A-x)
and sin(A-x)=0 if and only if A-x is an integer multiple of π.
Good luck with your head!
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Old 2019-04-29, 19:55   #4
wildrabbitt
 
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thanks.
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Old 2019-04-30, 22:18   #5
ewmayer
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Quote:
Originally Posted by Nick View Post
sin(A)cos(x) - cos(A)sin(x)=sin(A-x)
and sin(A-x)=0 if and only if A-x is an integer multiple of π.
Good luck with your head!
Or, in terms the way the OP phrased it, tan x = tan A if sin x = sin A and cos x = cos A, or if sin x = -sin A and cos x = -cos A.

Last fiddled with by ewmayer on 2019-04-30 at 22:19
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Old 2019-04-30, 22:45   #6
chalsall
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"Chris Halsall"
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Quote:
Originally Posted by ewmayer View Post
Or, in terms the way the OP phrased it, tan x = tan A if sin x = sin A and cos x = cos A, or if sin x = -sin A and cos x = -cos A.
I'm not sure you're a fan of Bill Maher, but there is a non-zero probability...
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