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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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