1. The problem statement, all variables and given/known data In the context of elliptical polarization,every book writes out this formula: (E_y/E_0y)^2 + (E_x/E_0x)^2 -2(E_y/E_0y)(E_x/E_0x) cos ε= (sinε)^2 where ε is the initial phase difference. After that they write this is the equation of an ellipse making an angle α with the E_x-E_y co-ordinate system such that tan 2α=[[2E_0x*E_0y]cos ε]/[(E_0x)^2 - (E_0y)^2] 2. Relevant equations 3. The attempt at a solution This is NOt a homework problem;but I want to clarify how does the 2nd relation concering tan 2α comes. I tried to understand by expanding tan 2α and by dividing RHS by (E_0x)^2 throught. But the factor cos ε is annoying. Can anyone please tell how the relation comes?