If A + C = B, then tan A tan B tan C =

tan A tan B + tan C

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tan B - tan C - tan A

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tan A + tan C - tan B

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-(tan A tan B + tan C)

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Solution

The correct option is B
tan B - tan C - tan A

$B = A + C \Rightarrow t a n B = t a n (A + C) \Rightarrow t a n B = \frac{t a n A + t a n C}{1 - t a n A t a n C} \Rightarrow t a n A t a n B t a n C = t a n B - t a n A - t a n C$

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