Can't figure how to prove when both source and observer are moving that the observed frequency is the product of the two independent cases below..
We know individual cases when source is moving and observer is still, the observed frequency is equal to fs/(1-(vs/c)*cos(theta_s)) where fs is the source frequency and theta_s is the angle between the source velocity and observer
Conversely when observer is moving, the observed frequency is fs*(1+(vo/c)*cos(theta_o))
The Attempt at a Solution
When you multiply both out, you get fo2=fs2*(c+vocos(theta_o))/(c-vscos(theta_s)) but they shouldnt be squared??