- #1

philnow

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## Homework Statement

A photon moves at an angle theta with respect to the x' axis in the frame S'. Frame S' moves with speed v with respect to frame S (along the x' axis). Calculate the components of the photon's velocity in S and verify that it's speed is c.

## The Attempt at a Solution

I break down the photon speed in S' into Ccos(theta) for X and Csin(theta) for y. There is no change from the transformation of frames with respect to the y-axis, only the x-axis. So the speed of the horizontal component of the photon in S frame is then

(Ccos(theta) + V) / (1 + (Ccos(theta)*V/C^2))

by velocity addition.

I would like to show that this squared, plus Csin(theta) squared should be equal to C^2. The problem is the algebra... whatever I do, I end up with cosines to odd and even powers that just won't simplify, so here I am. Any hints?