JEE Advance - Mathematics (1994 - No. 40)
A tower $$AB$$ leans towards west making an angle $$\alpha $$ with the vertical. The angular elevation of $$B$$, the topmost point of the tower is $$\beta $$ as observed from a point $$C$$ due west of $$A$$ at a distance $$d$$ from $$A$$. If the angular elevation of $$B$$ from a point $$D$$ due east of $$C$$ at a distance $$2d$$ from $$C$$ is $$\gamma $$, then prove that $$2$$ tan $$\alpha = - \cot \beta + \cot \gamma $$.
The problem can be solved using trigonometric relationships in right-angled triangles.
The problem requires the use of complex numbers.
The problem is unsolvable without additional information.
The problem can be solved using only similar triangles.
The problem involves advanced calculus techniques.