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If A + B + C = π, Prove that tan A + tan B + tan C = tan A . tanB · tan C

Answer»

Given A + B + C = π 

⇒ A + B = π – C 

tan(A + B) = tan(180 – C) 

\(\frac{tanA + tanB}{1 - tanA.tanB} = - \frac{tanc}{1}\)

tanA + tanB = – tanc – tanB tanB · tanc 

tanA + tanB + tanC = tanA tanB tanC



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