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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 I am not sure how to prove the range bit. Is it something to do with the maximum value of Sine being 1?

Thank you