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A particle is thrown over a triangle fro...

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

Text Solution

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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)) " "...(i)`
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`
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