Question

In an acute-angled triangle, $\cot B\cot C+\cot A\cot C+\cot A\cot B=$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

$\cot B\cot C+\cot A+\cot C+\cot A\cot B$

Since $A+B+C=\pi$

so, $A+B=\pi -C$

$\Rightarrow \cot (A+B)=\cot (\pi -C)$

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

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