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Q.

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 α and β be the base angles and θ the angle of projection, then

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a

tan2⁡θ=tan2⁡α+tan2⁡β

b

tan⁡θ=tan⁡α+tan⁡β

c

tan⁡θ=tan⁡αtan⁡β

d

tan⁡θ=tan⁡αtan⁡βtan⁡α+tan⁡β

answer is B.

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Detailed Solution

y=xtan⁡θ1−xR   .......(i)tan⁡α=yx            .......(ii)tan⁡β=yR−x    .....(iii)Solving Eqs. (i), (ii) and (iii), we gettan⁡θ=tan⁡α+tan⁡β
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