A man standing on a level plane observes the elevation of the top of a pole to be `theta`. He then walks a distance equal to double the height of the pole and then finds that the elevation is now `2theta`. The value of `cottheta` is

Options

A. `sqrt(2)+1`
B. `2-sqrt(3)/(2)`
C. `sqrt(2-1)`
D. `2+sqrt(3)`

Explanation

To solve the problem step by step, we will use trigonometric relationships and properties of right triangles.

### Step 1: Define Variables
Let:
- \( h \) = height of the pole
- \( d \) = distance from the man to the base of the pole when he observes the angle \( \theta \)

### Step 2: Set Up the First Triangle
...