Question

If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$

• A. 0
• B. 1
• C. 2
• D. -1

Answer 1

Answer: (B)

1

Answer 2

Given, $A+B+C=\pi$
$\Rightarrow A+B=\pi-C$
$\Rightarrow \cot (A+B)=\cot (\pi-C)$
$\Rightarrow \frac{\cot A \cot B-1}{\cot A+\cot B}=-\cot C$
$\Rightarrow \cot A \cot B-1=-\cot A \cot C-\cot B \cot C$
$\Rightarrow \cot A \cot B+\cot B \cot C+\cot C \cot A=1$