Here I'm using capital A to refer to the angle and lower-case a to refer to its tangent:
The identity you're trying to prove is equivalent to
(with lower-case a,b,c), so that's the same as
Now at this point I might not know how to proceed further if I hadn't seen the following at some point in the past. In the first place, the usual formula for the tangent of a sum implies with 30 seconds' more work that
and in the second place, if
So what you're being asked to prove is that if
We've see that the fact that
Moral: Don't do this problem if you've forgotten your trigonometry.
However, since the problem as stated doesn't mention trigonometry, I'm wondering if there's another way to do it that avoids that. Probably there is. The tangent function and the identities we used involve a particular way of parametrizing the circle, as
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