How does dither value affect the sine wave output of Altera NCO IP Core

if you look at equation:

s(nT) = Asin[2π(fO+ fFM)nT+ ϕPM+ ϕDITH)]

then adding constant for dith makes it no different to the equation from PM. The idea of dith is random values(+/- some suitable range) added in above equation in place of dith.

You actually don't need to do that to prove the concept, it is already proven but for own exercise dith is dith not a constant.