# Projectile motion maximum range

A plane is inclined at an angle A to the horizontal. A particle is projected up the plane with a velocity u at an angle B to the plane. the plane of projection is vertical and contains the the line of greatest slope

Prove that the range is a maximum when $$\displaystyle{B=\frac{1}{2}[(\frac{\pi}{2})-A]}$$

I found the time of flight to be $$\displaystyle{\frac{2uSinB}{gCosA}}$$ and then tried to find $$S_{x}$$ at this time. It was pretty long and im not sure how to prove the range bit. Is it something to do with the maximum value of Sine being 1?

Thank you