On 02/07/2014 03:36, Jim Thompson wrote:
On Tue, 1 Jul 2014 19:02:04 -0700, "garyr" wrote:


"Jim Thompson" wrote in
message ...
Nasty Math Problem of the Day...

http://www.analog-innovations.com/SED/MathNasty_2014_07_01.pdf

Any ideas?

...Jim Thompson
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| James E.Thompson | mens |
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I love to cook with wine. Sometimes I even put it in the food.

tan(a) + tan(b)
tan(a+b) = ----------------
1 - tan(a)*tan(b)

I think your only hope is a numerical approach. I suggest you state the
problem in the form: a = fa(x, y, p), b = fb(x, y, p) and post your query on
the SciPy newsgroup: http://scipy-central.org/.




I thinks Hobbs' move satisfies the Algebra. I'll report back later...
this is all about behavioral modeling/curve fitting.

...Jim Thompson

A few small substitutions will help you see the wood for the trees.

If I have read it right then the following will turn it into a
recognisable quadratic form.

Let
t = tan(theta)
x = Xw
y = 1-Yw^2
p = P/w

with the tan formula above simplifying and then later z = x/y to get a
quadratic form which subject to algebra slips I get to be :

(1-pt)z^2 + 2(p+t)z - 1 + pt = 0

Hence an expression for z = x/y as a function of p

Quick and dirty approx starting solution from
sqrt(1+x) = 1 + 2x/(4+x) x=1

Numerical might be less hassle than close form YMMV

--
Regards,
Martin Brown