The distance of three points on a pole from its foot are in A.P.  If the angles of elevation of these points from a point on the ground are α,βand γ, then cotβcotγ,cotγcotα and cotαcotβ are in

Given AB=a, AC=b, AD=ca,b,c are in A.P. ⇒2b=a+cAlso we have tanα=ax,tanβ=bx,tanγ=cx∴cotβ.cotγ+cotα.cotβ=xb.xc+xa.xb                                    =x2ba+cac=x2b.2bac                                      =2x2ac=2.xa.xc                                       =2cotα.cotγ