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The measurement of the expansion history of the Universe from the redshift unknown gravitational wave (GW) sources (dark GW sources) detectable from the network of LIGO-Virgo-KAGRA (LVK) detectors depends on the synergy with the galaxy surveys having accurate redshift measurements over a broad redshift range, large sky coverage, and detectability of fainter galaxies.In this work, we explore the possible synergy of the LVK with the spectroscopic galaxy surveys, such as DESI and SPHEREx, to measure the cosmological parameters which are related to the cosmic expansion history and the GW bias parameters. We show that by using the 3D spatial cross-correlation between the dark GW sources and the spectroscopic galaxy samples, we can measure the value of Hubble constant with about $2{{\ \rm per\ cent}}$ and $1.5{{\ \rm per\ cent}}$ precision from LVK+DESI and LVK+SPHEREx, respectively within the 5 yr of observation time with $50{{\ \rm per\ cent}}$ duty-cycle. Similarly, the dark energy equation of state can be measured with about $10{{\ \rm per\ cent}}$ and $8{{\ \rm per\ cent}}$ precision from LVK+DESI and LVK+SPHEREx, respectively. We find that due to the large sky coverage of SPHEREx than DESI, performance in constraining the cosmological parameters is better from the former than the latter. By combining Euclid along with DESI and SPHEREx, a marginal gain in the measurability of the cosmological parameters is possible from the sources at high redshift (z ≥ 0.9).