A cooler star would emit mostly in infrared range of the spectrum.
Emission of high temperature stars
High temperature stars like the Sun, which are approximately 6000 K at the surface, emit most of their radiation at visible wavelengths.
Emission of the cooler stars
In stark contrast to high temperature stars, the cooler stars emit most of their radiations in the infrared (IR) range.
Thus, we can conclude that, a cooler star would emit mostly in infrared range of the spectrum.
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