How Do You Prove the Second Formula Using the First?

[joebo]

can you tell me how to prove the second formula according to the first formula in the attachment?

 

[chrispb]

In the exponential of the first formula, rewrite the dot product in terms of things you know (magnitudes and angles) by picking/defining your q-vector to be along the z-hat direction. After that, write the measure in spherical coordinates and run with it.