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

Explanation

From triangle `y=x tan alpha`
`y=(R-x)tan beta`
` because y=x tan theta[1-(x)/(R)]rArr tan theta=(yR)/(x(R-x)) therefore tan theta=tan alpha+tan beta` (H.P)