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Tangents drawn from the point (c, d) to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` make angles `alpha` and `beta` with the x-axis.
If `tan alpha tan beta=1`, then find the value of `c^(2)-d^(2)`.

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To solve the problem, we need to find the value of \( c^2 - d^2 \) given that the tangents drawn from the point \( (c, d) \) to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) make angles \( \alpha \) and \( \beta \) with the x-axis, and that \( \tan \alpha \tan \beta = 1 \). ### Step-by-Step Solution: 1. **Equation of Tangents**: The equation of the tangents to the hyperbola from the point \( (c, d) \) can be expressed as: \[ y = mx + \sqrt{a^2 m^2 - b^2} ...
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