Lorentz factor for particle moving at angle

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ZedCar
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It's not a homework question, but I noticed on this webpage;

http://www.relativitycalculator.com/addition_relativistic_velocities.shtml

near the very bottom there is a section entitled, "What, therefore, would r & θ appear to be to an observor in relatively moving S'?"

Example 1

the formula then states:

tanθ' = u'y / u'x I understand why they're doing this. Though after this, can anyone explain the next part of the progression? Why have they applied a γ to the denominator of u'y but not to u'x ?

Thank you
 
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