Hey fobos3.
Can you show us what you have tried?
I tried solving for A in the two equations and then equating the result. This gives you something like:
I also tried expressing the two equations in exponential form but couldn't figure out how to solve it. I am not sure if it is possible to solve the system analytically.
P.S.
This is not a homework problem and it is related to calculating the frequency and amplitude of a sine wave using two recursive DFTs.