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

I found the time of flight to be [tex]\displaystyle{\frac{2uSinB}{gCosA}}[/tex] and then tried to find [tex]S_{x}[/tex] 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