Reproject GEOTIFF tiles from UTM to Plate Caree

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I need to reproject several GEOTIFF tiles in six different UTM zones from UTM to Plate Carree.

Output of gdalinfo of two sample tiles is enclosed. As is clearly seen they are the same type of projection but different UTM zone hence they are not the same projection. What I have been thinking of doing is reproject tiles from the other UTM zones to the tile of the first UTM zone and then mosaic all the tiles and then reproject to Plate Carree. I already have GIS software to do the reprojection and so my question relates to the validity of the approach. Will this give the best result or are there other approaches that will give better results?

My ultimate goal is to cut tiles of my choice of height/width from the mosaic.

Coordinate System is: PROJCS["WGS 84 / UTM zone 42N", GEOGCS["WGS 84", DATUM["WGS_1984", SPHEROID["WGS 84",6378137,298.257223563, AUTHORITY["EPSG","7030"]], AUTHORITY["EPSG","6326"]], PRIMEM["Greenwich",0], UNIT["degree",0.0174532925199433], AUTHORITY["EPSG","4326"]], PROJECTION["Transverse_Mercator"], PARAMETER["latitude_of_origin",0], PARAMETER["central_meridian",69], PARAMETER["scale_factor",0.9996], PARAMETER["false_easting",500000], PARAMETER["false_northing",0], UNIT["meters",1], AUTHORITY["EPSG","32642"]]

and 2nd tile -

Coordinate System is: PROJCS["WGS 84 / UTM zone 43N", GEOGCS["WGS 84", DATUM["WGS_1984", SPHEROID["WGS 84",6378137,298.257223563, AUTHORITY["EPSG","7030"]], AUTHORITY["EPSG","6326"]], PRIMEM["Greenwich",0], UNIT["degree",0.0174532925199433], AUTHORITY["EPSG","4326"]], PROJECTION["Transverse_Mercator"], PARAMETER["latitude_of_origin",0], PARAMETER["central_meridian",75], PARAMETER["scale_factor",0.9996], PARAMETER["false_easting",500000], PARAMETER["false_northing",0], UNIT["meters",1], AUTHORITY["EPSG","32643"]]



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