If the greatest value of the term independent of '\( x \)' in the expansion of \( \left(x \sin \alpha+a \frac{\cos \alph…

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