Given expression is `(xsinalpha+(cosalpha)/x)^10.`
General term in the given expansion can be given as,
`T_(r+1) = C(10,r) (xsinalpha)^(10-r)((cosalpha)/x)^r`
So, for the term independent of `x` ,
`=>10-r-r = 0`
`=>r = 5`
So, `6`th term will be independent of `x`.
`:. T_6 = C(10,5)(xsinalpha)^(10-5)((cosalpha)/x)^5`
`=(C(10,5))/2^5(2sinalphacosalpha)^5`
`=(C(10,5))/2^5(sin2alpha)^5`
Now, maximum value of `sin2alpha` will be `1`.
So, maximum value of the term independent of `x` will be `(C(10,5))/2^5.`
