If `x<0,\ y<0` such that `x y=1` , then `tan^(-1)x+tan^(-1)y` equals `pi/2` (b) `-pi/2` (c) `pi` (d) none of these

Explanation

To solve the problem, we need to find the value of \( \tan^{-1} x + \tan^{-1} y \) given that \( x < 0 \), \( y < 0 \), and \( xy = 1 \).

### Step-by-step Solution:

1. **Understanding the Condition**:
We know that both \( x \) and \( y \) are negative numbers, and they satisfy the equation \( xy = 1 \). This implies that \( y = \frac{1}{x} \).

**Hint**: Remember that if \( x < 0 \), then \( y \) must also be negative since their product is positive.
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