1. The problem statement, all variables and given/known data Solution set of the inequality (cot-1(x))2 -(5 cot-1(x)) +6 >0 is? 2. Relevant equations 3. The attempt at a solution Subs cot-1(x)=y We get a quadratic inequality in y. y2-5y+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?