A tower of height b subtends an angle `alpha` at a point on the same level as the food of the tower .At a second point , b meters above the first , the angle of depression of the foot pole and the finds that the elevation is now `2 theta ` .The value of cot `theta ` is

Options

A. b cot `alpha " tan " beta `
B. `b tan alpha tan beta `
C. `b tan alpha cot beta`
D. `b cot alpha cot beta`

Explanation

Let AB be the tower of height h, D be the point x away fron B and C be another point b m above D

In triangle ABD.
`h=x tan alpha`
In triangle BCE. `X= b cot beta`
from (1) and (2) we get
`therefore h=b tan alpha cot beta`