Final answer:
The suitable reagent for converting 1-bromo-1-methyl cyclohexane to bromomethyl cyclohexane is hydrogen gas with a platinum catalyst. This process is known as hydrogenation.
Step-by-step explanation:
The question at hand involves a chemical conversion from 1-bromo-1-methyl cyclohexane to bromomethyl cyclohexane. Among the reagents listed, hydrogen gas with a platinum catalyst is the appropriate choice for achieving such a transformation. This process, known as hydrogenation, involves the addition of hydrogen to the substrate 1-bromo-1-methyl cyclohexane to reduce the alkyl bromide to an alkane, thus forming bromomethyl cyclohexane.
The other reagents listed serve different purposes: Lithium aluminum hydride and sodium borohydride are commonly used for reduction reactions where they serve as hydride donors, not suitable for this transformation. Methylmagnesium bromide is a Grignard reagent used for carbon-carbon bond formation, not relevant to the process of hydrogenation.