How is the inter-tropical convergence zone related to the equatorial low-pressure trough?

The ITCZ is related to the equatorial zone of low pressure trough as this region is known as doldrums or the region of calms.

Explanation:

The Equator being in direct contact with the sun rays and hence, produces uneven heating of air as result the air above tends to rise and being dry and hotter this air mass rises and to poles and cool as result descends from the poles to order this low-pressure system. This region is seen as a region of calm winds as no motion takes place here as the convective current that forms the Hadley cells and their cyclic rotation with the rotation of the planet causes the winds being deflected to right in the northern hemisphere and to left in the southern hemisphere. Thus in this region, tropical cyclone is rare and seasonal cycle is more subtle. Some times this zone shifts away from the equator in northern summer due to the heavy arrangement of continents. Sometimes is thus called a monsoon thought. As compared to ITCZ the South Pacific Convergence Zone has a reverse orientation.

What exactly do you mean 

Answerair masses develop near the equator are warm; tropical air mass