Question : If $\tan A-\tan B-\tan C=\tan A \tan B \tan C$, what is the value of A in terms of B and C?
Option 1: $A = B + C$
Option 2: $A = 2 B - 2C$
Option 3: $A = B - C$
Option 4: $A=\frac{B-C}{2}$
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Correct Answer: $A = B + C$
Solution : Given, $\tan A-\tan B-\tan C=\tan A \tan B \tan C$ ⇒ $\tan A - \tan A \tan B \tan C = \tan B + \tan C$ ⇒ $\tan A(1-\tan B \tan C)= \tan B + \tan C$ ⇒ $\tan A = \frac{\tan B + \tan C}{1-\tan B \tan C}$ ⇒ $\tan A = \tan(B+C)$ $\therefore A = B + C$ Hence, the correct answer is $A = B + C$.
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