Projectile motion question totally stuck

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Thanks! I haven't seen that trig identity for years. It sure is handy in this problem.

emyt, if you are still watching, he has used
sin(x+y) + sin(x-y) = 2sin(x)cos(y)
You probably did it in high school using
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
and the same with y replaced by -y. These last identities are the commonly used "addition and subtraction formulas".