Correct. Good job.
I wonder if there is a proof of this that is not overly complex?
Edit:
Well, No. I just found the proof, and it's not beautiful for its simplicity.
You start with the Law of Sines, and 2 1/2 pages later you have a symmetrical expression for one side.
"Do not try this at home."
oh i am so sorry .....i mistook it for the eulers line....my bad...

Two consecutive numbers are given to A and B. when A is asked ‘do you know B’s number?’ A denies. when B is asked whether he knows A’s no., B also denies. at the very moment, A replies that he knows B’s number. what may be B’s number?