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

`tan alpha = (h)/(x), tan beta = (h)/(R - x)`
`tan alpha + tan beta = (h)/(x) + (h)/(R - x) = (hR)/(x(R - x)` (i)
Equation of trajectory
`y = x tan theta (1 - (x)/(R ))`
`h = (x tan theta(R - x))/(R ) rArr (hR)/(x(R - x) = tan theta` (ii)
`tan theta = tan alpha + tan beta`, proved