If the greatest value of the term independent of 'x' in the expansion of ${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$ is ${{10!} \over {{{(5!)}^2}}}$, then the value of 'a' is equal to :

Question

If the greatest value of the term independent of 'x' in the

expansion of ${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$ is ${{10!} \over {{{(5!)}^2}}}$, then the value of 'a' is equal to :