Solving trigonometric equation with tangent

[Gemm94]

Please help me the following equation, we need to calculate X relative to the other:
\begin{equation}
\tan{(2X-\phi_0)} = \frac{\rho\sin{\phi-a\sin{X}}}{\rho\cos{\phi}-a\cos{X}}
\end{equation}
Thank you very much!

[Country Boy]

What does "relative to the other" mean?  What "other"?

 

[math]tan(\alpha- \beta)= \frac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)}[/math]

so [math]tan(2X- \phi_0)= \frac{tan(2X)- tan(\phi_0)}{1+ tan(2X)tan(\phi_0)}[/math].

By the same formula

[math]tan(2X)= tan(X- (-X))= \frac{2tan(X)}{1- tan^2(X)}[/math]

Edited April 26, 2021 by Country Boy