The set of all the values of x satisfying the inequality (. (c o t)- 1 x .)2-7(.(c o t)- 1x.)+100 is

Question

The set of all the values of x satisfying the inequality (. (c o t)- 1 x .)2-7(.(c o t)- 1x.)+10>0 is (A) (.-∈ fty, cot 5.)∪(.cot 4,cot 2.) (B) (.cot 5,cot 4 ) (C) (.-∈ fty, cot 5.)∪(.cot 2,∈ fty.) (D) (c o t 2 , ∈ fty)

Tardigrade Admin · Accepted Answer

( cot -1 x-5)( cot -1 x-2)>0 ⇒ cot -1 x ∈(-∞, 2) ∪(5, ∞) ldots...(i) But, cot -1 x ∈(0, π)...(ii) Taking intersection of (I) and (ii), we get, ⇒ cot -1 x ∈(0,2) ⇒ x ∈( cot 2, ∞)

Q. The set of all the values of $x$ satisfying the inequality $((co t)^{- 1} x)^{2} - 7 ((co t)^{- 1} x) + 10 > 0$ is

$(- \in f t y, co t 5) \cup (co t 4, co t 2)$

$(co t 5, co t 4$ )

$(- \in f t y, co t 5) \cup (co t 2, \in f t y)$

$(co t 2, \in f t y)$

$(cot^{- 1} x - 5) (cot^{- 1} x - 2) > 0$
$\Rightarrow cot^{- 1} x \in (- \infty, 2) \cup (5, \infty) \dots$ ...(i)
But, $cot^{- 1} x \in (0, π)$ ...(ii)
Taking intersection of (I) and (ii), we get, $\Rightarrow cot^{- 1} x \in (0, 2)$
$\Rightarrow x \in (cot 2, \infty)$

Q. The set of all the values of x satisfying the inequality ((cot)−1x)2−7((cot)−1x)+10>0 is

(−∈fty,cot5)∪(cot4,cot2)

(cot5,cot4 )

(−∈fty,cot5)∪(cot2,∈fty)

(cot2,∈fty)