Question

difference between crest and trough of a wave

Answer 1

Crest of a wave-It is a point on the wave where the displacement of the medium is at a maximum. 
Trough of a wave-It is a point on the wave , if the displacement of the medium at that point is at a minimum.

Answer 2

the major difference between the crest and the trough of a wave is : 

trough : the displacement of the wave from its initial point is minimum. 

crest : the displacement of the wave from its initial point is maximum.