A) \[0\]
B) \[1\]
C) \[-1\]
D) \[\sqrt{3}\]
Correct Answer: B
Solution :
Expression \[=\cot {{9}^{o}},\,\,\cot {{27}^{o}},\,\,\cot {{63}^{o}},\,\,\cot {{81}^{o}}\] \[=\cot {{9}^{o}}.\cot {{27}^{o}}.\cot ({{90}^{o}}-{{27}^{o}})\] \[=\cot {{9}^{o}}.\cot {{27}^{o}}.\tan {{27}^{o}}.\tan {{9}^{o}}\] \[[\tan ({{90}^{o}}-\theta )=\cot \theta ;\,\,\cot ({{90}^{o}}-\theta )=\tan \theta ]\] \[=\cot {{9}^{o}}.\tan {{9}^{o}}.\cot {{27}^{o}}\tan {{27}^{o}}=1[\tan \theta .\cot \theta =1]\]
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