From the top of a cliff of height a, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height h. If `theta` be the angle of elevation, then prove that
`tan theta = sqrt(3-(2h)/(a))`.

Explanation

[ Hint : `CE = (h-a)/(tan theta)`…………..(1)
`tan 2theta = (a)/(AB) = (a)/(CE)`
or, `(2tan theta)/(1-tan^(2) theta) = (a)/(CE)`
or, ` (2 tan theta)/(1-tan^(2) theta) =(a)/((h-a)/(tan theta))` [ by (1) ]
`rArr " "tan theta(a-a tan^(2) theta - 2h +2a) = 0`
`rArr a - a tan^(2) theta-2h+2a = 0 [ because tan theta ne 0]`
`rArr tan^(2) theta = (3a-2h)/(a) " "rArr tan theta = sqrt(3-(2h)/(a))`. (proved)]