# 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?

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1. A = B + C
2. A = 2B - 2C
3. A = B - C
4. $$A = \frac{B-C}{2}$$

Option 1 : A = B + C
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## Detailed Solution

Given:

tan A - tan B - tan C = tan A tan B tan C

Formula Used:

tan (A - B) = $$\frac{tanA - tanB}{1+ tanAtanB}$$

Calculations:

⇒ tan A - tan B - tan C = tan A tan B tan C

⇒ tan A - tan B  = tan A tan B tan C + tan C

⇒ ​tan A - tan B  = tan C(tan A tan B + 1)

⇒ tan C = $$\frac{tanA-tanB}{1+tanAtanB}$$

⇒ tanC = tan(A - B)

⇒ C = A - B

⇒ A = B + C

⇒ Hence, The option 1 is correct
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