The ratio of `4^(th)` term and `5^(th)` term in the expansion of `(x+(sinx)/(x))^(6)` is `(16)/(3pi^(2))`, then x is equal to
(1) `(pi)/(2)`
(2) `-(pi)/(2)`
(3) `(pi)/(3)`
(4) Both (1) & (2)

Explanation

To solve the problem, we need to find the fourth and fifth terms in the expansion of \((x + \frac{\sin x}{x})^6\) and then set up the ratio according to the given condition.

### Step-by-Step Solution:

1. **Identify the terms**: The general term \(T_r\) in the expansion of \((x + y)^n\) is given by:
\[ T_r = \binom{n}{r-1} x^{n - (r-1)} y^{r-1} \]
...