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

Explanation

To find the greatest value of the term independent of \( x \) in the expansion of \( \left( x \sin \alpha + \frac{\cos \alpha}{x} \right)^{10} \), we will use the Binomial Theorem.

### Step-by-Step Solution:

1. **Identify the terms in the binomial expansion**:
The general term in the binomial expansion of \( (a + b)^n \) is given by:
\[
T_k = \binom{n}{k} a^{n-k} b^k
...