The formula for the relativistic Doppler shift is
where the sign of depends on whether the observer and the source are approaching or receding. In this problem, there are two sources, and one of them is receding and one of them is approaching, so the difference in wavelength is
where now is the speed (not the velocity) of a particle on the Sun's equator due to the Sun's rotation. Now,
so, we can rewrite equation (1) as
Now, we guess that the speed is tiny compared to the speed of light. This is intuitive, because one normally does not think of relativistic speeds when one thinks of the Sun macroscopically. Thus, we set
Then equation (2) becomes
We are given , , so we can easily solve for . We find that
This is indeed a nonrelativistic speed, so the approximation that was a good one. Therefore, answer (B) is correct.