Question

what is the angle of projection for maximum horizontal range

Answer 1

the maximum ranging angle is 45°....
as the formula of range is
R = (u^2 sin 2∅)/g
so, sin 2∅ is maximum in 45°....

Answer 2

The range of a projectile is given by

R=2v20sinθcosθg

and the maximum height is given by

h=v20sin2θ2g

For R=h we get

sinθcosθ=sin2θ

sinθcosθ−sin2θ4=0

sinθ(cosθ−sinθ4)=0

Therefore we get

sinθ=0 (trivial answer) or tanθ=4 (non-trivial answer)

tanθ=4

θ=760