Question

If A + C = B, then tanA tanB tanC =........

• A. tanA + tanB + tanC
• B. tanB- tanC- tanA
• C. tanA + tanB-tanC
• D. -(tanA+tanB+tanC)

Answer 1

The correct option is B tanB- tanC- tanA

$\Rightarrow$ $A+C=B$

Multiplying $\tan$ on both sides,

$\Rightarrow$ $\tan (A+C)=\tan B$

$\Rightarrow$ $\frac{\tan A+\tan C}{1-\tan A\tan C}=\tan B$

$\Rightarrow$ $\tan A+\tan C=\tan B(1-\tan A\tan C)$

$\Rightarrow$ $\tan A+\tan C=\tan B-\tan A\tan B\tan C$

$\Rightarrow$ $\tan A\tan B\tan C=\tan B-\tan C-\tan A$