A tower AB leans towards west making an angle `alpha ` with the vertical . The anlgular elevation of B , the topmost point of the tower is `beta` as obsreved from a point C due east of A at distance d from A.If the angular elevation of B from a pont D at a distance 2d due east of C is `gamma` , then prove that 2 tan `alpha` = cot `gamma` -cot `beta`

Options

A. `2 tan alpha = 2 cot beta - cot gamma `
B. `2 tan alpha = 3 cot beta - cot gamma`
C. ` tan alpha = cot beta - cot gamma`
D. None of these

Explanation

To solve the problem, we need to analyze the situation described in the question step by step.

### Step 1: Understanding the Geometry
We have a tower AB that leans towards the west, making an angle α with the vertical. We denote:
- A as the base of the tower,
- B as the top of the tower,
- C as a point due east of A at a distance d,
- D as a point due east of C at a distance 2d.
...