something I think is true but can't prove

[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).

[retina]

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

[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!

[wildrabbitt]

thanks.

[ewmayer]

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.

[chalsall]

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...