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A particle thrown over a triangle from o...

A particle thrown over a triangle from one end of a horzontal base falls on the other end of the base after grazing the vertExample if `alpha` and `beta` are the base angle of triangle and angle of projection is `theta`, then prove that `tan theta =tan alpha+tan beta`.

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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`
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