A) \[\cot \frac{A}{2}\cot \frac{B}{2}=4\]
B) \[\cot \frac{A}{2}\cot \frac{C}{2}=3\]
C) \[\cot \frac{B}{2}\cot \frac{C}{2}=1\]
D) \[\cot \frac{B}{2}\tan \frac{C}{2}=0\]
Correct Answer: A
Solution :
Trick: Take \[A=B=C={{60}^{o}},\] then \[\cot \frac{A}{2},\,\cot \frac{B}{2}\] and \[\cot \frac{C}{2}\] are in A.P. with common difference zero. Now option (b) satisfies.
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