if A,B and C are angles of a triangle, prove that tanA+tanB+tanC=tanAtanBtanC?

Question

pls show the steps

Answer 1

if A,B and C are angles of a triangle, we have A + B + C = pi.
Therefore, tan C = -tan(pi - C) = -tan(A + B)
= -(tan A+ tan B)/(1 - tan A tan B)
or: tan C = -(tan A+ tan B)/(1 - tan A tan B)
Time (1 - tan A tan B) to both sides:
tan C - tan A tan B tan C = -tan A - tan B
or: tan A + tan B + tan C = tan A tan B tan C

Answer 2

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Answer 3

tanC=-tan(Pi-C)=-tan(A+B)
=-(tanA+tanB)/(1-tanBtanA)
=>tanC-tanAtanBtanC=-tanA-tanB
=>tanA+tanB+tanC=tanAtanBtanC