I've encountered an equation that origins from a mechanical static problem containing a spring. I think the simplest formulation is the following:
$$ (a- \sqrt{b-c*cos(x)})*cos(d-x) = e*cos(f+x) $$
Trying to solve for x, where all the others are constants.
The first idea was to divide with cos(d-x), -a on both sides and square. You then get three terms on the right, two containing some form of const*cos(f+x)/cos(d-x). Wich you can simplify to something like:
$$const + tan(f+x)*const $$
This is done by cos(f+x-d+d) = and expanding by the cos(X+Y) rule.
I think my furthest attempt will achieve something in the realm of the following:
$$ cos(x) + const*tan(f+x)+const*tan^2(f+x) = const $$
I actually think both the tan terms will be dependent in the same way. I've been trying to find ways to solve similar equations but without success. You get some wiff of a simple quadratic equation but how do you handle the cos(x)?
If you get the left hand side as a sum of three trig terms would it be possible to express them as complex and then add them up?
From my standpoint and competence this problem has been surprisingly hard. I have posted a similar post on reddit without any success.
Thanks for any help in this matter.
