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 2019-04-28, 11:54 #1 wildrabbitt   Jul 2014 3×149 Posts 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).
2019-04-28, 12:19   #2
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

189E16 Posts

Quote:
 Originally Posted by wildrabbitt 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

 2019-04-28, 12:32 #3 Nick     Dec 2012 The Netherlands 176110 Posts 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!
 2019-04-29, 19:55 #4 wildrabbitt   Jul 2014 3×149 Posts thanks.
2019-04-30, 22:18   #5
ewmayer
2ω=0

Sep 2002
República de California

22×3×7×139 Posts

Quote:
 Originally Posted by Nick 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

2019-04-30, 22:45   #6
chalsall
If I May

"Chris Halsall"
Sep 2002

100111010001002 Posts

Quote:
 Originally Posted by ewmayer 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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