# How to solve a complicated algebraic equation with symbolic toolbox?

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Giuseppe on 9 Mar 2022
Edited: Torsten on 9 Mar 2022
Hi guys,
In the following image there are some expression of some parameters.
I need to solve the equality deriving from expression (17), i.e. in order to get .
I tried to solve the problem by hand but it involves many substitutions and it is full of computations.
Is there a way to perform this task by using the symbolic toolbox with as little effort as possible?

Torsten on 9 Mar 2022
Either
delta_w = k*pi (k integer)
or
delta_w = acos(((p1*e2)^2 + (p2*e1)^2 - (p1-p2)^2)/(2*p1*p2*e1*e2))
Torsten on 9 Mar 2022
Edited: Torsten on 9 Mar 2022
Since I don't have MATLAB available at the moment:
Do you get the same formula from MATLAB as the one from my hand calculation or
/ _____________________________________________________________\
| / / 2 2 2 2 2 2\ |
| / -\e1 *p2 - 2*e1*e2*p1*p2 + e2 *p1 - p1 + 2*p1*p2 - p2 / |
+/-2*atan| / ----------------------------------------------------------- |
| / 2 2 2 2 2 2 |
\\/ e1 *p2 + 2*e1*e2*p1*p2 + e2 *p1 - p1 + 2*p1*p2 - p2 /

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