Solution set of the inequality (cot-1(x))2 -(5 cot-1(x)) +6 >0 is?
The Attempt at a Solution
We get a quadratic inequality in y.
Using the wavy curve method, the solution set is,
So cot-1(x)<2 and cot-1(x)>3
Taking cot on both sides of the inequality,
x<cot2 and x>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?