Mark Wagner wrote in message <3a1ccd92@news.povray.org>...
> Wlodzimierz ABX Skiba wrote in message <3a1aade3$1@news.povray.org>...
> >Is there any person who can solve this for x ?
> >
> > (A*x-B)(cosx-sinx)=C
>
> Try graphing it and looking at the graph of the equation to find the
zeros.
> I'm fairly sure that the function cannot be solved for x, so if you
need the
> solution for x rather than the zeros, you're out of luck.

My equation could be transformated to:

(Ay+B)^2 * (1+sin(2*y)) = D^2

where A,B,D are not the same like at first and y=-x

there is simple but useless symbolic solution for this
using Taylor's formula we can describe sin as

sin(x)=sum(n:=0;n->infinity; (-1)^n * x^(2*n+1) / (2*n+1)!

this provide me to infinite exponent in equation
but this could be aproximated with finite n
for example Maple resolved it
(http://www.maplesoft.com/products/Maple6/maple6info.html):

x=(-1/(D+A))*(B-D)+(3/2*D/((D+A)^3))*(B-D)^2+(-1/6*D*(-11*A+16*D)/((D+A)
^5))*(B-D)^3+(1/8*D*(19*A^2+44*D^2-72*D*A)/((D+A)^7))*(B-D)^4+(-1/120*D*
(1524*D^3-3928*D^2*A+2692*D*A^2-361*A^3)/((D+A)^9))*(B-D)^5+O((B-D)^6)

where the last part O((B-D)^6) is the rest
with small B-D error will be small

I'm sure that there is one exact result in special range of A,B,D but
currently I work with completly different method of resolve my problem
therefore probably I will not profit from calculated result. Thanks to
all for effort.

ABX at babilon org

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