Picture a ball traveling at 10m/s along the x-axis. If you exert a force to the ball on the y-axis (so that the force is perfectly perpendicular to the direction of motion) it will now be also traveling on this axis at some velocity, its speed will remain the same relative to the x-axis but the total velocity increases.
But what if instead of a ball it was a photon? No force was applied on the x-axis, so I don't see why that velocity would change. But light's total speed always remains constant.
Would the x-velocity change to compensate for the added y-velocity? #science