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Solve and Trig functions


If I have the following two equations:

eq1 = a1 + b1 == Sin[fi];
eq2 = a2 + b2 == Cos[fi];

It is clear that

Tan[fi] == (a1+b1)/(a2+b2)

but how do I get Mathematica to recoginize this? This problem is trivial, but 
with more complicated expressions, the answer may not be immediately 
obvious.

Thanks,

Kevin

Kevin J. McCann
Johns Hopkins University APL


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