If the component lines whose combined equation is `px^(2)-qxy-y^(2)=0` make the angles `alphaand beta ` with x-axis , then find the value of tan `(alpha+beta)`.

Explanation

To solve the problem, we need to find the value of \( \tan(\alpha + \beta) \) given the combined equation of two straight lines \( px^2 - qxy - y^2 = 0 \).

### Step-by-Step Solution:

1. **Identify the coefficients**:
The given equation is \( px^2 - qxy - y^2 = 0 \). We can compare this with the general form of the equation of two straight lines through the origin, which is \( ax^2 + bxy + cy^2 = 0 \). Here, we have:
- \( a = p \)
- \( b = -q \)
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