List of top Mathematics Questions on Trigonometric Identities asked in UPSEE

From the top of a lighthouse, the angles of depression of two stations on the oposite sides of it at a distance d apart are $\alpha$ and $\beta$. The height of the lighthouse is

If $(1 + \tan \, 1^{\circ})(1 + \tan \, 2^{\circ}) ...... (1 + \tan \, 45^{\circ}) = 2^n$, then n is

For what interval of variation of $x$, the identity $arc \, \cos \frac{1 - x^2}{1 + x^2} = - 2 \, arc \, \tan \, x$ is true ?