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## Homework Statement

Solution set of the inequality (cot

^{-1}(x))

^{2}-(5 cot

^{-1}(x)) +6 >0 is?

## Homework Equations

## The Attempt at a Solution

Subs cot

^{-1}(x)=y

We get a quadratic inequality in y.

y

^{2}-5y+6>0

(y-2)(y-3)>0

Using the wavy curve method, the solution set is,

y∈(-∞,2) ∪(3,∞)

So cot

^{-1}(x)<2 and cot

^{-1}(x)>3

Taking cot on both sides of the inequality,

x<cot2 and x>cot3

x∈(-∞,cot2) ∪(cot3,∞)

Yet the answer is (-∞,cot3)∪(cot2,∞).

I'm guessing that in the step where I take cot on both sides, I'll have to change the inequality signs as arccot is a decreasing function. Is that where the problem lies?