The least positive solution of cot((π/3√3) sin 2x) = √3 lies in

Question

The least positive solution of cot((π/3√3) sin 2x) = √3 lies in (A) (0, (π/6)] (B) ((π/9), (π/6)) (C) ((π/12), (π/9)] (D) ((π/3), (π/2)]

Tardigrade Admin · Accepted Answer

cot ((π/3√3) sin 2x) = √3 ⇒ (π/3√3) sin 2x = nπ + (π/6), n ∈ Z ⇒ sin 2x = 3√3 n + (√3/2) For least positive solution, n = 0 ⇒ sin 2x = (√3/2) ⇒ 2x = (π/3) ⇒ x = (π/6)

Q. The least positive solution of $co t (\frac{π}{3 3} s in 2 x) = 3$ lies in

$(0, \frac{π}{6}]$

$(\frac{π}{9}, \frac{π}{6})$

$(\frac{π}{12}, \frac{π}{9}]$

$(\frac{π}{3}, \frac{π}{2}]$

$co t (\frac{π}{3 3} s in 2 x) = 3$
$\Rightarrow \frac{π}{3 3} s in 2 x = nπ + \frac{π}{6}, n \in Z$
$\Rightarrow s in 2 x = 33 n + \frac{3}{2}$
For least positive solution, $n = 0$
$\Rightarrow s in 2 x = \frac{3}{2}$
$\Rightarrow 2 x = \frac{π}{3}$
$\Rightarrow x = \frac{π}{6}$

Q. The least positive solution of cot(33​π​sin2x)=3​ lies in

(0,6π​]

(9π​,6π​)

(12π​,9π​]

(3π​,2π​]