Solve for `x` if `(cot^(-1)x)^2-3(cot^(-1)x)+2>0`

Explanation

`(cot^-1x)^2-3cot^-1x+2 gt 0`

`=>(cot^-1x)^2-2cot^-1x-cot^-1x+2 gt 0`

`=>cot^-1x(cot^-1x-2)-1(cot^-1x-2) gt 0`

`=>(cot^-1x-1)(cot^-1x-2) gt 0`

As `cotx` is a decreasing function,

`=>cot^-1x-1 gt 0 or cot^-1x-2 lt 0`

`:. x gt cot 1 and x lt cot2` is the solution for the given inequality.