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

Options

A. `2^(5)`
B. `(10!)/(5!)^(2)`
C. `(1)/(2^(5))(10!)/(5!)^(2)`
D. None of these

Answer

3

Explanation

`Cr(x sin alpha)^(10-r),x^(-1 cos alpha^(r))`
`Cr(sin alpha)^(10-r) (cos alpha)^(r ).(x)^(10-2r)`
"for independent of x"
`10-2r=0 rArr r= 5 `
`rArr T_(5+1)=C_(5)(sin alpha )^(5).(cos alpha)^(5) = C_(5)(sin 2 alpha)^(5)/(2)^(5)`
`rArr "greatest value" = (C_(5))/(2)^(5)`