A) \[\pm \,1\]
B) \[\pm \,\,2\]
C) \[\pm \,\,3\]
D) \[\pm \,\,4\]
Correct Answer: C
Solution :
Given, \[\tan \,{{1}^{o}}\tan {{2}^{o}}...\tan {{89}^{o}}={{x}^{2}}-8\] \[\Rightarrow \]\[\tan {{1}^{o}}\tan {{2}^{o}}...\tan {{44}^{o}}\tan {{45}^{o}}\cot {{44}^{o}}\] \[\Rightarrow \]\[...\,\cot {{2}^{o}}\cot {{1}^{o}}={{x}^{2}}-8\] \[\Rightarrow \]\[1={{x}^{2}}-8\Rightarrow {{x}^{2}}=9\] \[\Rightarrow \]\[x=\pm 3\]
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