A) \[(-\infty ,\cot 5)\cup (cot4,cot2)\]
B) \[(\cot 5,cot4)\]
C) \[(-\infty ,\cot 5)\cup (cot2,\infty )\]
D) \[(cot2,\infty )\]
Correct Answer: D
Solution :
Here,\[{{({{\cot }^{-1}}x)}^{2}}-7({{\cot }^{-1}}x)+10>0\] \[\Rightarrow \]\[(co{{t}^{-1}}x-5)(co{{t}^{-1}}x-2)>0\] \[\Rightarrow \]\[(co{{t}^{-1}}x>5or\,co{{t}^{-1}}x<2\] \[\Rightarrow \]\[x<\cot 5\,or\,x>\cot 2\] Since, \[x<\cot \,5\]does not satisfy the given inequality. \[\therefore \]\[x\in (cot2,\infty )\]
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