If tanA - tanB - tanC = tanA.tanB.tanC, what is the value of A in terms of B and C?

Answer: Option A

$$\begin{array}{rl}& \tan A-\tan B-\tan C=\tan A.\tan B.\tan C\\ & \tan A-\tan A.\tan B.\tan C=\tan B+\tan C\\ & \tan A=\frac{\tan B+\tan C}{1-\tan B.\tan C}\\ & \tan A=\tan \left(B+C\right)\\ & \text{On comparision,}\\ & A=B+C\end{array}$$