Two bodies are projected from the same point with same speed in the directions making an angle `alpha_(1)` and `alpha_(2)` with the horizontal and strike at same point in the horizontal plane through a point of projection. If `t_(1)` and `t_(2)` are their time of flights.Then `(t_(1)^(2)-t_(2)^(2))/(t_(1)^(2)+t_(2)^(2))`

Options

A. `(tan(alpha_(1)-alpha_(2)))/(tan(alpha_(1)+alpha_(2)))`
B. `(sin(alpha_(1)+alpha_(2)))/(sin(alpha_(1)-alpha_(2)))`
C. `(sin(alpha_(1)-alpha_(2)))/(sin(alpha_(1)+alpha_(2)))`
D. `(sin^(2)(alpha_(1)-alpha_(2)))/(sin^(2)(alpha_(1)+alpha_(2)))`

Answer

C

Explanation

`alpha_(1)+alpha_(2)=90^(@)rArrsin(alpha_(1)+alpha_(2))=1`
`t_(1)=(2u sin alpha_(1))/(g)`,`t_(2)=(2u sin alpha_(2))/(g)`