The possible values of θ ∈ (0, π) such that sin(θ ) + sin(4 θ ) + sin(7 θ ) = 0 are :

Question

The possible values of θ ∈ (0, π) such that sin(θ ) + sin(4 θ ) + sin(7 θ ) = 0 are : (A) (π/4), (5π/12), (π/2), (2π/3), (3π/4), (8π/9) (B) (2π/9), (π/4), (π/2), (2π/3), (3π/4),( 35π/36) (C) (2π/9), (π/4), (π/2), (2π/3), (3π/4),( 8π/9) (D) (2π/9), (π/4), (4π/9), (π/2), (3π/4),( 8π/9)

Tardigrade Admin · Accepted Answer

sin 4θ+ 2sin 4 θ cos 3θ = 0 ∵ θ, ∈(0, π) sin 4θ(1 + 2 cos 3 θ) = 0 sin 4θ= 0 or cos 3θ= - (1/2) 4θ = nπ ; n∈ I or 3θ = 2nπ ± (2π/3), n ∈ I θ = (π/4), (π/2), (3π/4) or θ = (2π/9), (8π/9), (4π/9)

Q. The possible values of $θ \in (0, π)$ such that sin( $θ$ ) + $s in (4 θ$ ) + $s in (7 θ) = 0$ are :

$\frac{π}{4}, \frac{5 π}{12}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{8 π}{9}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{35 π}{36}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{8 π}{9}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{4 π}{9}, \frac{π}{2}, \frac{3 π}{4}, \frac{8 π}{9}$

Q. The possible values of θ∈(0,π) such that sin(θ) + sin(4θ) + sin(7θ)=0 are :

4π​,125π​,2π​,32π​,43π​,98π​

92π​,4π​,2π​,32π​,43π​,3635π​

92π​,4π​,2π​,32π​,43π​,98π​

92π​,4π​,94π​,2π​,43π​,98π​

sin4θ+2sin4θcos3θ=0∵θ,∈(0,π) sin4θ(1+2cos3θ)=0 sin4θ=0 orcos3θ=−21​ 4θ=nπ;n∈I or3θ=2nπ±32π​,n∈I θ=4π​,2π​,43π​ or θ=92π​,98π​,94π​

Q. The possible values of $θ \in (0, π)$ such that sin( $θ$ ) + $s in (4 θ$ ) + $s in (7 θ) = 0$ are :

$\frac{π}{4}, \frac{5 π}{12}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{8 π}{9}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{35 π}{36}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{π}{2}, \frac{2 π}{3}, \frac{3 π}{4}, \frac{8 π}{9}$

$\frac{2 π}{9}, \frac{π}{4}, \frac{4 π}{9}, \frac{π}{2}, \frac{3 π}{4}, \frac{8 π}{9}$