A) 1
B) \[cot\text{ }A\text{ }cot\text{ }B\text{ }cot\text{ }C\]
C) \[-1\]
D) 0
E) \[cot\text{ }A+cot\text{ }B+cot\text{ }C\]
Correct Answer: A
Solution :
\[A+B+C=180{}^\circ \] \[\Rightarrow \] \[cot(A+B+C)=\] \[\frac{\Sigma \cot A\cot B-1}{\cot A\cot B\cot C-\Sigma \cot A}=\frac{1}{0}\] \[\Rightarrow \] \[\cot A\cot B\operatorname{co}C-\Sigma \cot A=0\] \[\Rightarrow \] \[\frac{\cot A+\cot B+\cot C}{\cot A\cot B\cot C}=1\]
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