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Re: How do u go about doing this---?

• To: mathgroup@smc.vnet.net
• Subject: [mg10932] Re: [mg10844] How do u go about doing this---?
• From: jpk@max.mpae.gwdg.de
• Date: Thu, 12 Feb 1998 20:16:19 -0500

> 
> Let f(x) = sin(x)+cos(y)
>                 -----------------
>                 sin(x) - cos(y)
> 
> Show that
>                 (df/dx)^2 + (df/dy)^2    =
> 
>                 2+cos(2(x-y))+cos(2(x+y))
>                 -----------------------------------
>                             (sin(x)-cos(y))^4
> 
> 
> Thanks,
> 
> L.
> 
> 
> 
Hi, it can't be shown because with
f[x,y]->(Sin[x]+Cos[y])/(Sin[x]-Cos[y])

one gets for

D[f[x,y],{x,2}]+D[f[x,y],{y,2}]=

(-4*(Cos[x]^2*Cos[y] + Sin[x]*Sin[y]^2))/(Cos[y] - Sin[x])^3

what is clearly different from Your "result"

Hope that helps
  Jens