The value(s) of θ, which satisfy the equation: 2 cos 3 3 θ+3 cos 3 θ+4=3 sin 2 3 θ is/are -

Question

The value(s) of θ, which satisfy the equation: 2 cos 3 3 θ+3 cos 3 θ+4=3 sin 2 3 θ is/are - (A) (2 n π/3)+(2 π/9), n ∈ I (B) (2 n π/3)-(2 π/9), n ∈ I (C) (2 n π/5)+(2 π/5), n ∈ I (D) (2 n π/5)-(2 π/5), n ∈ I

Tardigrade Admin · Accepted Answer

2 cos 3 3 θ+3 cos 3 θ+4-3 sin 2 3 θ ⇒ ( cos 3 θ+(1/2))(2 cos 2 3 θ+2 cos 3 θ+2)=0 ⇒ cos 3 θ=-(1/2) ⇒ 3 θ=2 n π ± (2 π/3) ⇒ θ=(2 n π/3) ± (2 π/9)

Q. The value(s) of $θ$ , which satisfy the equation : $2 cos^{3} 3 θ + 3 cos 3 θ + 4 = 3 sin^{2} 3 θ$ is/are -

$\frac{2 nπ}{3} + \frac{2 π}{9}, n \in I$

$\frac{2 nπ}{3} - \frac{2 π}{9}, n \in I$

$\frac{2 nπ}{5} + \frac{2 π}{5}, n \in I$

$\frac{2 nπ}{5} - \frac{2 π}{5}, n \in I$

$2 cos^{3} 3 θ + 3 cos 3 θ + 4 - 3 sin^{2} 3 θ$
$\Rightarrow (cos 3 θ + \frac{1}{2}) (2 cos^{2} 3 θ + 2 cos 3 θ + 2) = 0$
$\Rightarrow cos 3 θ = - \frac{1}{2} \Rightarrow 3 θ = 2 nπ \pm \frac{2 π}{3}$
$\Rightarrow θ = \frac{2 nπ}{3} \pm \frac{2 π}{9}$

Q. The value(s) of θ, which satisfy the equation : 2cos33θ+3cos3θ+4=3sin23θ is/are -

32nπ​+92π​,n∈I

32nπ​−92π​,n∈I

52nπ​+52π​,n∈I

52nπ​−52π​,n∈I