Set of values of ' α ' in [0,2 π] for which m= log (x+(1/x))(2 sin α-1) ≤ 0, is -

Question

Set of values of ' α ' in [0,2 π] for which m= log (x+(1/x))(2 sin α-1) ≤ 0, is - (A) [(π/6), (5 π/6)] (B) ((π/6), (5 π/6)) (C) (0, (π/6)) ∪((5 π/6), π) (D) ((5 π/6), (7 π/6))

Tardigrade Admin · Accepted Answer

log (x+(1/x))(2 sin α-1) ≤ 0 ∵ x+(1/x)>2 so 2 sin α-1 ≤ 1 2 sin α-1>0 ⇒ 2 sin α ≤ 2 sin α>(1/2) ⇒ sin α ≤ 1 α ∈((π/6), (5 π/6))

Q. Set of values of ' $α$ ' in $[0, 2 π]$ for which $m = lo g_{(x + \frac{1}{x})} (2 sin α - 1) \leq 0$ , is -

$[\frac{π}{6}, \frac{5 π}{6}]$

$(\frac{π}{6}, \frac{5 π}{6})$

$(0, \frac{π}{6}) \cup (\frac{5 π}{6}, π)$

$(\frac{5 π}{6}, \frac{7 π}{6})$

$lo g_{(x + \frac{1}{x})} (2 sin α - 1) \leq 0$
$∵ x + \frac{1}{x} > 2$
so $2 sin α - 1 \leq 1&2 sin α - 1 > 0$
$\Rightarrow 2 sin α \leq 2& sin α > \frac{1}{2}$
$\Rightarrow sin α \leq 1$
$α \in (\frac{π}{6}, \frac{5 π}{6})$

Q. Set of values of ' α ' in [0,2π] for which m=log(x+x1​)​(2sinα−1)≤0, is -

[6π​,65π​]

(6π​,65π​)

(0,6π​)∪(65π​,π)

(65π​,67π​)