A projectile fired with velocity u at right angle to the slope which is inclined at an angle $\mathrm{\theta }$ with horizontal. The expression for R is

$\mathrm{R}=\mathrm{OP}=\frac{1}{2}\mathrm{gsin}{\mathrm{\theta T}}^2$
As initial velocity along inclined plane is zero while reaching P, ⊥ ^r displacement for inclined plane is zero
$\begin{array}{l}0=\mathrm{uT}-\frac{1}{2}\mathrm{gcos}{\mathrm{\theta T}}^2\Rightarrow \mathrm{T}=\frac{2\mathrm{u}}{\mathrm{gcos}\mathrm{\theta }}\\ \therefore \mathrm{R}=\frac{1}{2}\mathrm{gsin}\mathrm{\theta }\frac{4{\mathrm{u}}^2}{{\mathrm{g}}^2{\cos }^2\mathrm{\theta }}=\frac{2{\mathrm{u}}^2}{\mathrm{g}}\tan \mathrm{\theta sec}\mathrm{\theta }\end{array}$