ABCD is a trapezium such that `A B||C Da n dC B` is perpendicular to them. If `/_A D B=theta,B C=p ,a n dC D=q` , show that `A B=((p^2+q^2)sintheta)/(pcostheta+qsintheta)`

Explanation

To solve the problem, we need to show that \( AB = \frac{(p^2 + q^2) \sin \theta}{p \cos \theta + q \sin \theta} \).

### Step-by-Step Solution:

1. **Understanding the Trapezium**:
- We have a trapezium \( ABCD \) where \( AB \parallel CD \) and \( BC \perp AB \) and \( CD \).
- Let \( \angle ADB = \theta \), \( BC = p \), and \( CD = q \).

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