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!

Hi everyone, I have a problem when doing an approximation. The problem comes in the final results that I have to demonstrate two functions below equal each other frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}. \begin{equation} \frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}. \end{equation} I have checked the two functions by numerical calculation to a graph and see that two functions give exactly the same shape with the $\phi\leq \pi$ as shown in the figure. \begin{figure}[!t] \centering \includegraphics[scale=1]{Nonuniform-ka20-E.eps} \caption{Comparison between two functions} \end{figure}