The solution set of the equation 4sin θ cos ⁡ θ -2cos ⁡ θ -2√3sin ⁡ θ +√3=0 in the interval (0 , 2 π ) is

Question

The solution set of the equation 4sin θ cos ⁡ θ -2cos ⁡ θ -2√3sin ⁡ θ +√3=0 in the interval (0 , 2 π ) is (A)  (3 π /4) , (7 π /4)  (B)  (π /3) , (5 π /3)  (C)  (3 π /4) , π , (π /3) , (5 π /3)  (D)  (π /6) , (5 π /6) , (11 π /6)

Tardigrade Admin · Accepted Answer

4sin θ cos â¡ θ -2cos â¡ θ -2√3sin â¡ θ +√3=0 2cos θ (2 sin â¡ θ - 1)-√3(2 sin â¡ θ - 1)=0 (2 cos θ - √3)(2 sin â¡ θ - 1)=0 ⇒ sin θ =(1/2),cos â¡ θ =(√3/2) θ =(π /6),(5 π /6),(11 π /6)

Q. The solution set of the equation $4 s in θ cos θ - 2 cos θ - 23 s in θ + 3 = 0$ in the interval $(0, 2 π)$ is

${\frac{3 π}{4}, \frac{7 π}{4}}$

${\frac{π}{3}, \frac{5 π}{3}}$

${\frac{3 π}{4}, π, \frac{π}{3}, \frac{5 π}{3}}$

${\frac{π}{6}, \frac{5 π}{6}, \frac{11 π}{6}}$

$4 s in θ cos θ - 2 cos θ - 23 s in θ + 3 = 0$
$2 cos θ (2 s in θ - 1) - 3 (2 s in θ - 1) = 0$
$(2 cos θ - 3) (2 s in θ - 1) = 0$
$\Rightarrow s in θ = \frac{1}{2}, cos θ = \frac{3}{2}$
$θ = \frac{π}{6}, \frac{5 π}{6}, \frac{11 π}{6}$

Q. The solution set of the equation 4sinθcos⁡θ−2cos⁡θ−23​sin⁡θ+3​=0 in the interval (0,2π) is

{43π​,47π​}

{3π​,35π​}

{43π​,π,3π​,35π​}

{6π​,65π​,611π​}