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

Correct option is 42π9,π4,4π9,π2,3π4,8π9

Questions

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

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π4,5π12,π12,2π3,3π4,8π9

2π9,π4,π2,2π3,3π4,35π36

2π9,π4,π2,2π3,3π4,8π9

2π9,π4,4π9,π2,3π4,8π9

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detailed solution

Correct option is D

sin⁡θ+sin⁡4θ+sin⁡7θ=0⇒ 2sin⁡4θcos⁡3θ+sin⁡4θ=0⇒ sin⁡4θ(2cos⁡3θ+1)=0⇒ sin⁡4θ=0 or cos⁡3θ=−1/2=cos⁡(2π/3)⇒ θ=π4,π2,3π4 or 3θ=2π/3, 2π 2π/3⇒ θ=2π9,π4,π2,4π9,3π4,8π9

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

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