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AM,GM,HM Inequality

If A,B,C ar...

Question

If $A, B, C$ are the angles of $△ A B C$ then $cot A . cot B + cot B . cot C + cot C . cot A$ is equal to

A

0

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B

1

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C

2

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D

- 1

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Solution

The correct option is B $1$
We know that
$t a n A + t a n B + t a n C = t a n A . t a n B . t a n C$
Dividing both sides by $t a n A . t a n B . t a n C$
$\Rightarrow \frac{1}{t a n A . t a n B} + \frac{1}{t a n B . t a n C} + \frac{1}{t a n A . t a n C} = 1$
$\Rightarrow c o t A . c o t B + c o t B . c o t C + c o t A . c o t C = 1$
Therefore Answer is $B$

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