Question

If value of x which satisfy equation ${\left({\cot }^{-1}x\right)}^2-3\left({\cot }^{-1}x\right)+2>0$ is $x<\cot a$ or $x>\cot b$.
Find the value of $a+b$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

${\left({\cot }^{-1}x\right)}^2-3\left({\cot }^{-1}x\right)+2>0$
$\Rightarrow$ ${\cot }^{-1}x<1$ or ${\cot }^{-1}x>2$
$\Rightarrow$ $x>\cot 1$ or $x<\cot 2$
$\Rightarrow$ $x<\cot 2$ or $x>\cot 1$