Question

If $A,B,C$ are angle of a triangle $ABC$ and $\tan A\tan C=3;\tan B\tan C=6$; then which of the following is correct?

• A. $A=\frac{\pi }{4}$
• B. $\tan A\tan B=2$
• C. $\frac{\tan A}{\tan C}=3$
• D. $\tan B=2\tan A$

Answer 1

Answer: (D)

$\tan B=2\tan A$

We have,

In $\Delta ABC$

$\tan A.\tan C=3.....\left(1\right)$

$\tan B.\tan C=6......\left(2\right)$

Now, Divide by (1) to (2) and we get,

$\frac{\tan A\tan C}{\tan B\tan C}=\frac{3}{6}$

$\Rightarrow \frac{\tan A}{\tan B}=\frac{1}{2}$

$\Rightarrow \tan B=2\tan A$

Hence, this is the correct answer.