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The secondary formula of college entrance examination mathematics, such as tana+tan b+ tanc = tanatanbanc.
tanA+tanB = tan(A+B)*( 1-tanA tanB)

Then tan(A+B)=tan(pi-C)=-tanC.

get tana+tan b+ tanc =-tanc( 1-tana tanb)+tanc = tanatanbanc。

Therefore, this formula has application premise, that is, A+B+C =π or three angles of a triangle.

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