A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If alpha and beta be the base angles and theta be the angle of projection, prove thattam theta=tanalpha+tanbeta.

A particle is thrown over a triangle from one end of a horizontal base

1.	A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If alpha and beta be the base angles and theta be the angle of projection, prove thattam theta=tanalpha+tanbeta.
Answer» Solution :The situation is SHOWN in figure. From figure, we have `tanalpha+tanbeta=(y)/(x)+(y)/(R-x)` `tanalpha+tanbeta=(YR)/(x(R-x))""…….(i)` But EQUATION of trajectory is `y = xtantheta[1-(x)/(R)]` `TANTHETA=(yR)/(x(R-x))""...........(ii)` From Eqs. (i) and (ii),`tantheta=tanalpha+tanbeta`