Find the greatest value of the term independent of `x` in the expansion of `(xsinalpha+(cosalpha)/x)^(10)` , where `alpha in R`.

Explanation

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`

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