Verify/prove that:

(cotA+cotB)/(tanA+tanB)+(1-cotAcotB)/(1-tanAtanB) = 0

2 answers

tan(A+B) = (tanA+tanB)/(1-tanAtanB)

that should get you started.
I'm sorry, I just still don't understand exactly how you even got tan(A+B) = (tanA+tanB)/(1-tanAtanB). What happened to the cotA+cotB, 1-cotAcotB, and 0? If you simplified the original identity, then how did you do that? Because what I did was expand the cot and tan into sin and cos, but then I get stuck and I am unable to match (cotA+cotB)/(tanA+tanB)+(1-cotAcotB)/(1-tanAtanB) to 0.