Question

In a $\Delta$$ABC,O$ is a point inside the triangle such that $\angle OBC=\angle OCA=\angle OAB={15}^0$ then value of $\cot A+\cot B+\cot C$ is

• A. $2-\sqrt{3}$
• B. $\sqrt{2}-1$
• C. $\sqrt{2}+1$
• D. $2+\sqrt{3}$

Answer 1

Answer: (D)

$2+\sqrt{3}$

$\frac{1}{\tan A}+\frac{1}{\tan B}+\frac{1}{\tan C}$
$\frac{\tan A\tan B+\tan C\tan B+\tan C\tan A}{\tan A\tan B\tan C}$