Question: Prove that tanA + tanB + tan C = tanA tan B tan C, where A, B and C are angles of a triangle.
Solution: tan A + tan B + tan C = tan (A + B) (1 - tan A tan B) + tan C
= tan (180 - C) (1 - tan A tan B) + tan C
= -tan C (1 - tan Atan B) + tan C
= -tan C + tan C tan A tan B + tan C
= tan A tan B tan C (proven)
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