The height of a tower is h and the angle of elevation of the top of the tower is a. On moving a distance h/2 towards, the tower, the angle of elevation becomes 0. The value of cotα

1. The height of a tower is h and the angle of elevation of the top of the tower is a. On moving a distance h/2 towards, the tower, the angle of elevation becomes 0. The value of cotα - cot β is

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By: anil on 05 May 2019 01.50 am

Here, $$angle$$ACB = $$alpha$$ and $$angle$$ADB = $$eta$$ AB = tower = $$h$$ metre and CD = $$frac{h}{2}$$ metre From $$ riangle$$ABC => $$tan alpha = frac{AB}{BC} = frac{h}{BC}$$ => $$BC = h cot alpha$$ ----------Eqn(1) From $$ riangle$$ABD => $$tan eta = frac{AB}{BD} = frac{h}{BC - CD}$$ => $$tan eta = frac{h}{h cot alpha - frac{h}{2}}$$ => $$h cot alpha - frac{h}{2} = h cot eta$$ => $$h (cot alpha - cot eta) = frac{h}{2}$$ => $$cot alpha - cot eta = frac{1}{2}$$

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