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$Tan (A - B) + Tan (B - C) + Tan (C - A) =$

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$TanA TanB TanC$

$CotA CotB CotC$

$Tan (A - B) Tan (B - C) Tan (C - A)$

$0$

answer is C.

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Detailed Solution

$\begin{array}{rcl} \tan (A - B) + \tan (B - C) + \tan (C - A) \\ \begin{array}{rcl} A - B + B - C + C - A & = & 0 \end{array} \\ \tan (A - B) + \tan (B - C) + \tan (C - A) \\ = & \tan (A - B) \tan (B - C) \tan (C - A) \end{array}$

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