Point A is h m above the ground level BC. DC represents the tower. The angle of elevation of the top of the tower from point A is α and the and the angle of depression of the base of the tower from point A is β. Prove that the height of the tower is h(tan α + tan β) / tan β

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In the end you get 

Height = h (1 + tan α cot β)

⇒ Height = h (1 + tan α/ tan β)

 ⇒ Height = h (tan β + tan α)/ tan β

Hence proved!

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