Question

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)`

Answer 1

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