Q83 / 150 · MHT CET 2018 · Mathematics

If $A, B, C$ are the angle of $Δ A B C$ then $\cot A \cot B + \cot B \cot C + \cot A \cot C =$

A
$0$
Correct answer
B
$1$
C
$2$
D
$- 1$

Solution

Given

A + B + C = π

\Rightarrow A + B = π - C

\Rightarrow \cot (A + B) = \cot (π - C)

\Rightarrow \frac{\cot A \cot B - 1}{\cot A + \cot B} = - \cot C

\Rightarrow \cot A \cot B - 1 = - \cot A \cot C - \cot B \cot C

\Rightarrow \cot A \cot B + \cot B \cot C + \cot A \cot C = 1

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

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