A ladder rests against a vertical wall at inclination `alpha` to the horizontal. Its foot is pulled away from the wall through a distance p so that it's upper end slides q down the wall and then ladder make an angle `beta` to the horizontal show that ` p/q = ( cos beta - cos alpha)/(sin alpha - sin beta)`.

Explanation

To solve the problem, we will use trigonometric identities and properties of right triangles. Let's break down the solution step by step.

### Step 1: Understand the Setup
We have a ladder of length \( L \) leaning against a vertical wall. Initially, it makes an angle \( \alpha \) with the horizontal. The foot of the ladder is pulled away from the wall by a distance \( p \), and the top slides down the wall by a distance \( q \), resulting in the ladder making an angle \( \beta \) with the horizontal.

### Step 2: Determine the Initial Position
In the initial position, we can express the horizontal and vertical distances in terms of \( L \), \( \alpha \):
- The horizontal distance from the wall to the foot of the ladder (point A) is:
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