In a triangle tan A + tan B + tan C =
tan A . tan B . tan C
In a triangle A + B + C = 180
A + B = 180 - C
Taking for an both sides
Tan (A + B) = tan (180 - C)
tanA+tanB1−tanA.tanB = tanC
tan A + tan B = - tan C + tan A tan B tan C
tan A + tan B + tan C = tan A tan B tan C
Option C is correct