Question

If in any $\Delta ABC;\cot\frac{A}{2},\cot\frac{B}{2},\cot\frac{C}{2}$ are in A.P., then

• A. $\cot\frac{A}{2}\cot\frac{B}{2} = 4$
• B. $\cot\frac{A}{2}\cot\frac{C}{2} = 3$
• C. $\cot\frac{B}{2}\cot\frac{C}{2} = 1$
• D. $\cot\frac{B}{2}\tan\frac{C}{2} = 0$

Answer 1

Answer: (B)

$\cot\frac{A}{2}\cot\frac{C}{2} = 3$

Answer 2

Sol. Trick: Take $4\sqrt{3} =$ then $\Delta PQR + \Delta PRS)$ and$\cot C/2$ are in A.P. with common difference zero. Now option (2)

satisfies.