Answer :

Given ABC is a triangle, so A + B + C = 180°


Now applying tan on both sides


tan (A+B +C) = tan (180°)


tan (A + B + C) = 0 ----- (1)


Also given tan A + tan B + tan C = 0 ------ (2)


As per the formula of tan (A+B+C)



Now,


[from equation (1) ]




[from equation (2) ]


By cross multiplying


-tan A tan B tan C = 0


tan A tan B tan C = 0


therefore


Hence cot A cot B cot C = 0


The answer is option D.

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