Let $A B C$ be an acute-angled triangle and let $D$ be the midpoint of $B C$. If $A B=A D$, then $\tan (B) / \tan (C)$ equals

• A

  $\sqrt{2}$
• B

  $\sqrt{3}$
• C

  2
• Correct answer
  D

  3

Solution

Using M - N Rule $$ \begin{array}{l} (1+1) \cot (\pi-B)=1 \cdot \cot B-\cot C \\ 3 \cot B=\cot C \\ \frac{\tan B}{\tan C}=3 \end{array} $$

Hence, the correct answer is option: 'D'.