Obtain "alpha" from this equation

[geno]

This is my first post here, salutes to everybody .

Well, how could i obtain "alpha" from this equation:

Rho = (A * tan [ (90- alpha) * (PI/ (2*180)) ] ) / ( [(1-n)/(1+n)]^(Ec/2) )


Where "n" is:n = Ec * sin( alpha * (PI/180) )

And:
"A" and "Rho" are known values.
"Ec" is a constant value: Ec = 0.08181.

Some help would be pretty much appreciated, i'm being stucked with this for two days

Edit: Hm... i'm not sure if this post should've been posted in this thread, sorry if not. In such case, please, somebody tell me where i should post it, or move it.

[geno]

Well, this problem seems to be quite difficult, at least for me.
I've could not dedicate to this problem many time, i've been very busy with a lot of other more urgent things.

The only advance i've been able to do in the little time i've had available for this (this evening concretely ) is shown below, but first i have to apologize, because the equation i posted originally was not totally correct, so i sorry indeed if someone has been trying to solve it.

Here i go with the original, and correctly wrote this time, equation:

Rho = A * [ tan [ (90- alpha) * (PI/ (2*180)) ] / [(1-n)/(1+n)]^(Ec/2) ] ^N

Where "n" is: n = Ec * sin( alpha * (PI/180) )

And:
"A", "Rho" and "N" are known values.
"Ec" is a constant value: Ec = 0.08181.

And here are the steps i've done today:

1.- Rho/A = [ tan [ (90- alpha) * (PI/ (2*180)) ] / [(1-n)/(1+n)]^(Ec/2) ] ^N

2.- [Rho/A]^1/N = tan [ (90- alpha) * (PI/ (2*180)) ] / [(1-n)/(1+n)]^(Ec/2)

3.- [Rho/A]^1/N = tan [ (45- alpha/2) * (PI/ 180) ] / [(1-n)/(1+n)]^(Ec/2)

4.- (PI/180) is there to convert the angle into Radians, so i can get it out of there:

[Rho/A]^1/N = tan [ (45- alpha/2) ] / [(1-n)/(1+n)]^(Ec/2)

5.- We have that :
tan(45- alpha/2) = ( tan (45) - tan (alpha/2) ) / ( 1 + tan(45)*tan(alpha/2) ) = (1 - tan(alpha/2) ) / ( 1 + tan(alpha/2) ) , aplying this result we have:

[Rho/A]^1/N = [(1 - tan(alpha/2) ) / ( 1 + tan(alpha/2) )] / [(1-n)/(1+n)]^(Ec/2)

6.- I'm going to substitute "n" getting out (PI/180), so now n = Ec * sin( alpha )
And then:

[Rho/A]^1/N = [(1 - tan(alpha/2) ) / ( 1 + tan(alpha/2) )] / [(1 - Ec*sin( alpha ))/(1+ Ec*sin( alpha ))]^(Ec/2)

This final equation still looks menacing , i'm not sure about persisting in this way, but perhaps somebody could see something in it i cannot at this moment, i hope that .

[Soarer]

hi, i am quite sure that you posted in a wrong forum. May any moderator move this topic.