The result `tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy))` is true when the value of xy is `"………."`

Explanation

To solve the problem, we need to determine the condition under which the equation

\[ \tan^{-1} x - \tan^{-1} y = \tan^{-1} \left( \frac{x - y}{1 + xy} \right) \]

holds true.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation involves the inverse tangent (arctan) function. For the equation to be valid, the expression on the right-hand side must be defined.

2. **Identifying the Denominator**:
The right-hand side has a denominator of \(1 + xy\). For the arctan function to be defined, this denominator must not be zero. Therefore, we need to ensure:

\[ 1 + xy \neq 0 \]

3. **Finding the Condition**:
From the inequality \(1 + xy \neq 0\), we can rearrange it to find:

\[ xy \neq -1 \]

4. **Considering the Valid Range**:
To ensure that the expression remains valid and does not approach undefined behavior, we need to consider when \(1 + xy\) is greater than zero:

\[ 1 + xy > 0 \]

This simplifies to:

\[ xy > -1 \]

5. **Conclusion**:
Thus, the value of \(xy\) must be greater than \(-1\) for the original equation to hold true.

### Final Answer:
The value of \(xy\) is greater than \(-1\).