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

Explanation

The situation is shown in figure. From figure, we have
`tan alpha+tan beta=y/x+y/(R-x)`
`tan alpha+tan beta=(yR)/(x(R-x))` (1)
But equation of trajectory is `y=x tan theta[1-x/R]`
`tan theta=[(yR)/(x(R-x)]` (ii)
From eqs.(i) and (ii), `tan theta=tan alpha+tan beta`