If R is the horizontal range for θ inclination and h is the maximum height . . .

Question : If R is the horizontal range for θ inclination and h is the maximum height reached by the particle, show that the maximum range is given by [R²/8h]+2h

Doubt by Shruti 

Solution : 

We know 
R=u²sin2θ/g
h=u²sin²θ/2g
R_max (Maximum Range) = u²/g

To Prove : 
R_max=[R²/8h]+2h

Proof : 

RHS
[R²/8h]+2h

Substituting sin2θ=2sinθcosθ

= R_max

= LHS

LHS=RHS
Hence Proved.