Question

If ${\left({\cot }^{-1}x\right)}^2-8{\cot }^{-1}x+15>0$ then x lies in the interval

• A. $(\cot 5,\cot 3)$
• B. $(-\infty ,\cot 5)$
• C. $(\cot 2,\infty )$
• D. $R-[\cot 5,\cot 3]$

Answer 1

The correct option is D $R-[\cot 5,\cot 3]$

${\left({\cot }^{-1}x\right)}^2-8{\cot }^{-1}x+15>0$
$\Rightarrow ({\cot }^{-1}x-3)({\cot }^{-1}x-5)>0$
$\Rightarrow co{t}^{-1}x\in (-\infty ,3)\cup (5,\infty )$
Thus, $cotx\in R-[cot5,cot3]$