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

A. A = B + C

B. A = 2B - 2C

C. A = B - C

D. $${\text{A}} = \frac{{{\text{B}} - {\text{C}}}}{2}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & \tan A - \tan B - \tan C = \tan A.\tan B.\tan C \cr & \tan A - \tan A.\tan B.\tan C = \tan B + \tan C \cr & \tan A = \frac{{\tan B + \tan C}}{{1 - \tan B.\tan C}} \cr & \tan A = \tan \left( {B + C} \right) \cr & {\text{On comparision,}} \cr & A = B + C \cr} $$