Question

If $\text{A + C = B,}$ then $\text{tan A tan B tan C =}$

• A. $\text{tan A tan B + tan C}$
• B. $\text{tan B – tan C – tan A}$
• C. $\text{tan A + tan C – tan B}$
• D. $\text{-(tan A tan B + tan C)}$

Answer 1

The correct option is B

$\text{tan B – tan C – tan A}$

Finding the value of $\mathbf{\text{tan A tan B tan C}}$ :

Given, $\text{A + C = B}$

Apply $\text{“ tan”}$on both sides,

$\text{tan(A + C) = tan B}$

$\text{⇒ (tan A + tan C)/(1 – tan A tan C) = tan B}\left(\because tan\left(A+B\right)=(tanA+tanB)/(1\; –tanAtanB)\right)$

$\text{tan A + tan C = tan B(1 – tan A tan C)}$

$\text{tan A + tan C = tan B – tan A tan B tan C}$

$\mathbf{\text{∴ tan A tan B tan C = tan B – tan A – tan C}}$

Hence, option $\left(\text{B}\right)$ is correct.