Prove that the area of the parallelogram formed by the lines `xcosalpha+ysinalpha=p ,xcosalpha+ys inalpha=q ,xcosbeta+ysinbeta=ra n dx cosbeta+ysinbeta=si s+-(p-q)(r-s)cos e c(alpha-beta)dot`

Explanation

To prove that the area of the parallelogram formed by the lines \( x \cos \alpha + y \sin \alpha = p \), \( x \cos \alpha + y \sin \alpha = q \), \( x \cos \beta + y \sin \beta = r \), and \( x \cos \beta + y \sin \beta = s \) is given by

\[ \text{Area} = \pm (p - q)(r - s) \csc(\alpha - \beta), \]

we can follow these steps:

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