Relationship between electric field components: ellipse

[boddhisattva]

Homework Statement

Given an electric field:

E=Ex*ex+Ey*ey

with

Ex=cos(kx-wt)
Ey=cos(kx-wt+e)

where e is the phase difference

Show that

Ex^2 + Ey^2 - 2*Ex*Ey*cos(e) = ( sin(e) )^2

Homework Equations

Ex=cos(kx-wt)
Ey=cos(kx-wt+e)

The Attempt at a Solution

Was unable to find a solution with trigonometric relations

 

[vela]

That equation can't possibly be true. The units on the two sides don't match.