Question
If $$\tan A + \tan B + \tan C = \tan A \cdot \tan B \cdot \tan C$$ then
A.
$$A, B, C$$ must be angles of a triangle
B.
the sum of any two of $$A, B, C$$ is equal to the third
C.
$$A + B + C$$ must be an integral multiple of $$\pi $$
D.
None of these
Answer :
$$A + B + C$$ must be an integral multiple of $$\pi $$
Solution :
$$\eqalign{
& \tan \left( {A + B + C} \right) = 0\,\left( {{\text{from the question}}} \right) \cr
& \therefore \,\,A + B + C = n\pi . \cr} $$