A) 2
B) 3
C) 4
D) 5
E) \[\frac{1}{2}\]
Correct Answer: E
Solution :
Given that \[cosA=cos\text{ }B\text{ }cos\text{ }C\] \[\Rightarrow \] \[\cos \{180{}^\circ -(B+C)\}=\cos B\cos C\] \[\Rightarrow \] \[-cos\text{ }B\text{ }cos\text{ }C+sin\text{ }B\text{ }sin\text{ }C=cos\text{ }B\text{ }cos\text{ }C\] \[\Rightarrow \] \[\frac{\cos B\cos C}{\sin B\sin C}=\frac{1}{2}\] \[\Rightarrow \] \[cot\text{ }B\text{ }cot\text{ }C=\frac{1}{2}\]
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